Physics Flashcards
(123 cards)
1
Q
How do you derive v = u + at?
A
Rewrite acceleration as the rate of change of velocity, and then integrate with respect to time.
2
Q
How do you derive s = x + ut +1/2(at^2)
A
Rewrite velocity as the rate of change of displacement, and substitute in v = u + at. Integrate with respect to time.
3
Q
How do you derive s = 1/2(v + u)t
A
Rearrange v = u + at for a, and substitute into s = x + ut + 1/2(a(t^2))
4
Q
How do you derive v^2 = u^2 +2as
A
Rearrange v = u + at for time, and then substitute into s = x + ut + 1/2(at^2)
5
Q
Is g a vector?
A
No, g is a magnitude of 9.807, it only has a direction when used as a value for acceleration.
6
Q
What is a projectile?
A
A projectile is an object in motion that, given an initial velocity, is acted on exclusively by air resistance and the acceleration due to gravity.
7
Q
What is a trajectory?
A
A trajectory is the path a projectile follows.
8
Q
How can a trajectory be analysed?
A
A trajectory can be analysed by splitting the motion into 2 components x and y, which act independently but both depend on time.
9
Q
What does the horizontal component of a trajectory depend on?
A
It depends on a constant velocity provided at the start of the motion, and is given from x = vt
10
Q
What does the vertical component of a trajectory depend on?
A
The vertical component depends on the acceleration due to gravity, and is given from
S = ut + 1/2 at^2
11
Q
How can we find a formula for the trajectory?
A
We can find this by putting the vertical component in terms of the horizontal component, or in other words, y in terms of x instead of t.
12
Q
What are the two ways the maximum height can be found?
A
One way is to differentiate the trajectory equation or vertical displacement equation to find the maximum value.
The other is, given the motion is symmetrical, the time of flight can be recorded and halfed, as an object will reach its maximum value halfway through its flight time.
13
Q
What is angular motion?
A
Angular motion is analogous to linear motion, however occurs around an axis instead of on a line.
14
Q
What is the best coordinate system for angular motion and why?
A
Polar coordinates, as it measures the distance to the axis of rotation and the angle of displacement.
15
Q
What is angular displacement, and how is it found?
A
The change in angle around an axis of rotation. It can be found from theta = s/r, where s is the linear displacement and r is the radius from the axis of rotation.
16
Q
What is angular velocity, and how is it found?
A
The rate of change of angular displacement. It can be found from omega = d(theta)/dt
17
Q
What is the period of angular motion, and how is it found?
A
The period is the time taken for 1 full revolution, and is given as T = 2*pi/(omega)
18
Q
What direction does angular velocity act?
A
It acts perpendicular to the linear velocity and the angular acceleration, which due to the cross product causes it to act above the circle.
19
Q
What happens to the linear velocity when the angular velocity is constant?
A
When the angular velocity is constant, the linear speed will be too, however due to the rotation causing a change in the angle, there is a change in the linear velocity, and therefore an angular acceleration.
20
Q
What is uniform circular motion?
A
When both the distance from the axis of rotation and the angular velocity are constant.
21
Q
What is radial acceleration and how is it found?
A
Radial acceleration is another term for angular acceleration, and is an acceleration directed towards the axis of rotation. It is found as the rate of change for angular velocity, with an equation of a = -w^2r or
a=-v^2/r
22
Q
What is the centripetal force, and how is it found?
A
As there is an acceleration pointing in, there is a force pointing in too, this being the centripetal force. It can be found by introducing Newton’s second law, and is given as F = mv^2/r =mw^2r
23
Q
What hapens if the centripetal force can’t be provided?
A
If there is nothing to maintain the required centripetal force to match the radial acceleration, the change in linear velocity will stop and therefore will have no direction change, causing the object to leave the angular motion tangential to the moment in which it stopped.
24
Q
What is a force?
A
A force is an interaction between two objects or between an object and its environment. It is a vector quantity, measured in Newtons (N), and must be exerted in a specific direction.
25
What are the different types of forces?
Push/Contact Force: Directly applied to an object.
Pull/Tension Force: Applied through another object (e.g., pulling a rope).
Friction Force: Resistance between two surfaces.
Normal Force: Force applied perpendicular to the surface of contact.
26
What are long distance forces?
Long-distance forces can act between objects even when separated by space, such as gravitational force, electromagnetic attraction, and strong and weak nuclear forces.
27
What are resultant forces?
The resultant force is the single force that represents the combined effect of multiple forces acting on an object, showing the total direction and magnitude of the motion.
28
How are forces combined?
Forces acting directly parralel will combine/cancel out, and those acting at an angle will combine using trigonometry.
29
What is the equation for the normal force on a slope?
The normal force is given by:
N=mgcos(θ), where m is mass, g is gravitational acceleration, and θ is the angle of the surface.
30
What is friction?
Friction is the resistance to motion between two surfaces, caused by microscopic irregularities and chemical interactions at the atomic level.
31
What are the 3 rules of friction?
A minimum force is needed to overcome friction and set an object in motion.
Heavier objects require more force to move due to increased contact with the surface.
Smoother surfaces have less friction, requiring less force to maintain motion.
32
How does friction behave over time as a force is applied?
As force is applied, friction increases to match it. Once the applied force surpasses the maximum static friction, motion begins, and the force required to maintain movement remains constant.
33
What is static friction?
Static friction is the force that prevents movement when two surfaces are stationary. It is determined by the normal force and has a maximum value before motion begins.
34
What is the formula for static friction?
F is less than or equal to Fs = μsN
F is the applied force (N), Fs is the static friction force (N), μs is the coefficient of static friction (dimensionless), n is the normal force (N).
35
What is the kinetic friction?
Kinetic friction occurs when an object is moving. It has a constant magnitude once motion begins, determined by the normal force and the coefficient of kinetic friction.
36
What is the formula for kinetic friction?
Fk=μkn,
where:
Fk is the kinetic friction force (N), μk is the coefficient of kinetic friction (dimensionless), n is the normal force (N).
37
What is force equilibrium?
Equilibrium occurs when there are no net forces acting on an object.
38
What is inertia?
Inertia is an object’s resistance to having its motion changed, meaning an object will continue in motion at a constant velocity unless acted upon by an external force.
39
What is Newton's first law?
Newton's First Law states:
"A body acted on by no net forces moves with a constant velocity."
This means objects in equilibrium will continue moving with constant velocity unless acted on by an unbalanced force.
40
When does Newton's first law hold?
Newton's First Law holds in inertial reference frames, which are frames of reference that are not accelerating. It doesn't hold in non-inertial (accelerating) frames.
41
What is an inertial reference frame?
A reference frame is inertial if it is moving with a constant velocity relative to another inertial frame. Frames that are accelerating are non-inertial.
42
What role does friction play in Newton's first law?
Friction often provides an unbalanced force that slows down or stops motion, disrupting the equilibrium and constant velocity predicted by Newton's First Law.
43
What is Newton's Second Law?
Newton's Second Law states:
"If a net force acts on an object, the object will accelerate in the direction of the force applied."
44
How are a force and an acceleration related in newton's second law?
The force applied to an object is directly proportional to its acceleration, and the mass of the object plays a significant role. This relationship is expressed by the equation:
f=ma,
where f is the force, m is the mass, and a is the acceleration.
45
Why does mass affect acceleration?
Mass affects acceleration because an object with more mass has more inertia, meaning it resists changes in motion. Therefore, more force is required to accelerate a heavier object.
46
What is the formula for Newton's Second Law?
The formula for Newton's Second Law is:
a=f/m,
where:
a is the acceleration, f is the force applied, m is the mass of the object.
47
How does gravity vary at different scales?
Gravity behaves differently depending on the scale. At the human scale, it simply causes objects to fall to the ground, but at larger scales, such as between planets or stars, it can maintain orbits and other complex interactions.
48
What are the two rules of gravity?
Gravity diminishes to zero at an infinite scale.
Gravity depends linearly on the masses of the objects involved.
49
What is Newton's law of gravity?
Newton's Law of Gravity states that the force of gravity between two objects is calculated using the formula:
F= Gm1m2/r^2
Where:
F is the gravitational force between the objects (N) G is the universal gravitational constant (6.67430×10−11m3kg−1s−2) m1 and m2 are the masses of the two objects (kg) r is the distance between the two objects (m)
50
How does gravity affect the motion of objects?
Gravity causes objects to accelerate towards each other. For example, it pulls objects towards the Earth, causing them to fall to the ground, and it maintains the orbits of planets around stars.
51
What is simple harmonic motion?
Simple Harmonic Motion occurs when the force acting on an object is proportional to its displacement and acts in the opposite direction.
52
What is Hooke's Law and how does it relate to simple harmonic motion?
Hooke's Law is given by
F=−kx,
where:
F is the force (N)
k is the restoring force constant (kg/s²)
x is the displacement (m)
It describes the restoring force that acts on an object undergoing simple harmonic motion.
53
What is the general equation for displacement in SHM?
The general solution for displacement in SHM is:
x=Acos(ωt+φ)
Where:
x is the displacement
A is the maximum displacement
ω is the angular frequency
t is time
φ is the phase, which indicates the starting angular position of the motion
54
How do you find the velocity in SHM?
To find the velocity at any point in SHM, differentiate the displacement equation.
55
How do you find the acceleration in SHM?
To find the acceleration at any point in SHM, differentiate the displacemetn equation twice.
56
What is the simple pendulum and how does it demonstrate SHM?
A simple pendulum consists of a mass m attached to the end of a weightless string of length l.
The angle the string makes with the vertical is theta. The restoring force is the component of weight, mgsinθ, and the motion of the pendulum can be described as SHM for small angles.
57
What is the general equation for analysing simple pendulum SHM?
ω=sqrt(g/l)
58
How do you approach a moment of inertia problem for a complex rotating object like a hammer?
Break it into core shapes, and analyse the moment of inertia separately. For example, a hammer would consist of a rod and a point mass rotating at a length equivalent to the rod length.
Then add these moments of inertia.
59
What is work energy?
The energy change an object experiences when a force F pushes an object a distance D.
60
How is work energy calculated?
w = Fs
61
What are the three different types of work, and how are they achieved?
1. Positive work - achieved when the force has a component in the direction of displacement
2. Zero work - achieved when the force acts perpendicular to the direction of displacement
3. Negative work - achieved when the force has a component in the opposite direction of displacement
62
How do you find the work energy from a force-displacement graph?
The energy can be found by finding the area under a force-displacement graph.
63
How do you find the work energy when a force is changing as it is applied?
Take the integral of the force with respect to displacement.
64
How does an object having work done on it undergo a change in velocity.
The force applied over the distance causes an increase in the object's energy, which is converted to kinetic energy and results in an increase in velocity.
65
What is the equation for kinetic energy?
K=(1/2)mv^2
66
What is the work energy theorem?
The work energy theorem states that the work done on an object equals the change in kinetic energy of the object. It gives the equation:
W(total) = (delta)K
67
What is power in work energy, and what are the two ways it can be found for work energy?
In work energy, power is the rate at which work is done, and the average work power and instantaneous work power can be found differently. The average is taken by dividing the total work energy by the total time in which it is applied. The instantaneous is found by taking the derivative of the work energy, which gives P=F*v.
68
What is the formula for the work energy of a spring?
W = 1/2kx^2
69
What is the requirement for an object's energy to be potential?
The object's energy must solely depend on its position.
70
What is the potential energy in a gravitational field equation?
U = mgy
71
What happens when a gravitational field does work on an object?
It experiences a change in gravitational potential energy due to its new displacement.
72
What is total mechanical energy, is it conserved, and how is it calculated?
Total mechanical energy is the sum of a system's kinetic and potential energy. It is a conserved quantity when gravity alone acts on the system. It is calculated as:
E = K + U
73
What is elastic potential energy, and how is it calculated?
Elastic potential energy is the energy stored by an elastic object when a force is applied. It is given as:
U = (1/2)kx^2
Where k is the spring constant (or similar), and x is the displacement (amount it has been compressed/stretched).
74
What is an energy diagram?
It is a graph that is divided into regions depicting kinetic and potential energy, representing total mechanical motion.
75
What 4 things are true when work is done by a conservative force?
The work done can be expressed as an energy diagram.
The work done is reversable.
The work done is independent of the path taken.
The work done is 0 if the path taken is independent.
76
How is a conservative force calculated using a potential energy function depending on the dimensions in which it acts?
In one dimension, the conservative force is found by taking the potential energy function derivative with respect to displacement.
In two dimensions, the components conservative force is found by taking two derivatives of the potential energy graph with respect to the x and y directions. These forces can then be combined.
In three dimensions, a nabula operator must be used and so is not explored in first year.
77
How does gravitational potential energy work at large scales, and how is it calculated?
At large scales, gravitational potential energy is the energy required to move a mass m to a distance outside the gravitational field.
The range of gravity is infinite, and setting this infinity point as 0, the gravitational potential energy at any point in the field can be found from:
W = =−(Gm1m2)/r
78
What is momentum, and how is it calculated?
Momentum is the product of an object's mass and velocity, and is given as:
P = mv
79
What is impulse and how is it calculated?
Impulse is both the change in momentum an object experiences, and the product of an average force and the time in which it acts. It is given as:
J = F*t
or
J = m(v-u)
80
What is the area under a force-time graph?
The area under a force-time graph is the impulse of an object.
81
What is the rule for conservation of linear momentum?
In an isolated, system the total linear momentum is constant.
82
How can a collision be analysed using momentum?
We can analyse the momentum before and after a collision to find the velocities of the objects involved.
83
What are the two types of collision?
Elastic collisions, where the kinetic energy is conserved.
Inelastic where the kinetic energy is not conserved.
84
What is angular momentum, and how is it found?
Angular momentum is analogous to linear momentum, just as angular momentum is for linear momentum.
It is found by multiplying the linear momentum with the radius of the path:
L = rp
It can also be found using
L=I(omega)
If the axis of rotation is symmetrical.
85
What is torque, and how is it found?
Torque is the rate of change for angular momentum over time, and so is analogous to force in angular motion. It is given as:
τ = Fr
or
T = Ia
86
What is a force's action line and lever arm?
A force's action line is a straight line across which a force acts. The line between the point on this action line at which the axis of rotation is parralel, and the point of rotation is called the lever arm.
87
What is moment of inertia, and how is the equation for the moment of inertia derived?
Moment of inertia is known as the reluctance of an object to change its rotational motion, with each point in a mass having its own radius it rotates around. As there are infinite points in a mass, the moment of inertia is given as:
I=∑mr^2
or
I = ∫r^2 dm
88
What is the conservation of angular momentum, and what does this mean when the radius of rotation changes?
The conservation of angular momentum states that in the absence of net torques, the total angular momentum is conserved. As dL/dt = T, when torque = 0, dL/dt = 0 and therefore the angular momentum is constant.
As I=∑mr^2 and L=I(omega), the angular momentum depends on the radius of rotation, and decreasing it leads to an increase in angular velocity (omega).
89
What is rotational energy, and how is it found?
Rotational energy occurs when work is done to induce/increase rotational motion, rotational energy will occur. It is an angular analogue to kinetic energy, and is given as:
E = (1/2)I(omega)^2
90
What is an event?
A 'happening' that occurs at a certain space and time.
91
What is a reference frame?
A method of observation specific to each observer, containing a clock and a coordinate syste, relative to them
92
What is the velocity of an observer relative to their own reference frame?
0ms^(-1)
93
What are Einstein's Postulates?
1. The laws of physics are the same in every frame of reference
2. The speed of light in a vacuum is the same in all inertial frames of reference and is independent of its source.
94
How does Galilean coordinate transformation work?
It works by measuring one reference frame using another, taking the distance of a point in one reference frame as the sum of its distance in another, plus the velocity at which that second frame is moving compared to the first frame.
95
What is relativity of simultaneity?
Relativity os simultaneity explains how events seen as happening at the same time in one reference frame may not happen the same way in another.
It works when events in different spacial positions occuring at the same time are occur at different times due to an observer moving relative to them viewing the events.
96
How do you derive a moment of inertia equation?
Put the moment of inertia as an integral {r^2 dm, and then find the ratio of a point mass on that mass with the ratio of a tiny volume over the whole thing, and then integrate the rearranged formula with respect to the radius.
97
How is time typically measured, and what is the benefit of using this method of measurement?
Using a light clock, which records the time taken for light to be reflected off a mirror and hit a reciever. The benefit is that light defines time well in terms of the speed of light constant, and so has a consistent scale across which time is measured.
98
What is the equation for the lorentz factor?
y=1/sqrt(1-v^2/c^2)
99
What is the equation for time dilation, and how is it derived?
t'=ty
Start by considering a moving time clock. In the frame of reference of the time clock, it has a velocity of t0 = 2d/c (where d is the length of the time clock).
An observer will see the clock move horizontally, with the light following a path L instead of just moving straight up and down. For an observer, the light takes a time of t=2L/c
Bear in mind that the light clock will have moved a distance of ut, with u being the velocity of the light clock.
Put L in terms of the distance d light travels, and the distance the clock travels using pythagoras theorem.
Substitute and collect like terms.
100
What is the twin paradox, and how is it resolved?
If one member of a pair of twins gets in a spaceship and the other stays on earth and the spaceshup travels at relativistic speeds, one twin will be older than the other, but which is it? While the spaceship is moving at a relativistic speed, from its perspective, earth is moving at this high speed.
This is resolved by including a third observer (the stars, for example) and seeing whether each twin is moving in a non-inertial reference frame compared to the third observer. The one that is will not age.
101
What is proper time?
The time measured in the same reference frame as the clock (or whatever is measuring the time).
102
What is length contraction and how is it calculated?
Length contraction is the apparant reduction of length for an object moving at relativistic speeds to an observer, and is calculated from l'=l/y where y is the lorentz factor.
103
How is the length contraction equation derived?
Start by measuring the distance a beam of light travels in the reference frame of a light clock. This will give a length l0=1/2ct0 (as it takes time to be reflected back).
In an observer's reference frame, light takes a different amount of time to reach the detector and be reflected back, as it travels different distances.
The distance to reach the reflector is d=l+ut1
where d is the distance light travelled (ct1)
The distance back is d=l-ut1, as the detector moves to meet the light.
Now, combine these halfs into the total observed time, and use the time dilation equation.
104
What is the train tunnel paradox?
If a train is moving at relativistic speeds and enters a tunnel of a smaller length than it, from the train's perspective the tunnel's length will contract and it will not fit.
From the tunnel's perspective, the train will shrink lengthwise and will fit inside the tunnel.
This is solved by considering that simultanious events may occur in one reference frame, but not the other. The train's front being inside the tunnel while the back is inside is a simultanious event for the tunnel, but not the train.
In the train's frame of reference, the end of the tunnel is reached at a different time to when the end of the train enters.
As a result both answers are true at the same time, with there being no contradiction as the only thing that matters is the reference frame.
105
What is a spacetime diagram and what is it composed of?
A spacetime diagram is a method of showing how an object moves through space and time. It shows that an object moving more through space will move less through time and vice-versa.
It is composed of a plane, representing the "present moment of time"
A "future cone" representing all points in space and time that can be reached from the current position (It has an outer line at 45 degrees to the space and time axes, representing the speed of light).
A "past cone" representing all points in space and time that an object could have come from to reach the current position (It has an outer line at 45 degrees to the space and time axes, representing the speed of light).
106
What are lorentz transformations for two frames of reference moving relative to eachother?
For the displacement of a point in a frame S' from a frame S:
x' = y(x-ut)
As the new displacement is equal to the full displacement minus the amount the new frame is ahead of the old (adjusted for relativistic speeds using the lorentz factor).
For the new time:
t' = y(t-ux/c^2)
For the new velocity:
v'x = (vx-u)/(1-(uvx/c^2))
For the old velocity:
vx = (v'x+u)/(1+(uv'x/c^2))
107
Why is momentum relativistic, and how is relativistic momentum calculated?
Momentum can be relativistic as it relies on velocity, which without relativity implies a maximum momentum (which simply isnt true). It can be calculated from:
P = ymv
108
What is the relativistic mass, and how is it calculated?
Relativistic mass is an intepretation that the mass of an object increases with its velocity (linking special and general relativity), and is calculated from:
m(rel) = ym
109
Why is kinetic energy relativistic, and how is relativistic kinetic energy calculated?
Kinetic energy is relativistic as it relies on velocity, meaning if relativity wasn't taken into account then it would imply a maximum kinetic energy (which isn't true). It is calculated from K = (y-1)mc^2
110
What is the rest energy of a particle, and how is it calculated?
The rest energy of a particle is the energy associated with a particles mass, and is a base energy a particle has independent of movement. It is calculated as simply
E(rest) = mc^2
111
How is a particle's total energy calculated, and what can it be simplified to?
E(total) = K + E(rest)
E(total) = (y-1)mc^2 + mc^2
E(total) = ymc^2
112
What is the total energy for a massless particle?
E = pc
113
How is temperature quantified at a microscopic level?
Temperature is seen as the velocity of particles in a substance.
114
How is temperature quantified at a macroscopic level?
Observing properties temperature effects allows a scale to be built around such properties, extrapolating back to find an absolute minimum and then build a temperature scale around this.
One example of this is with pressure against degrees celcius, with -273.15 degrees celcius being the 0 value of an absolute temperature scale.
115
What is 0K in celcius?
-273.25 degrees celcius
116
What is thermal equilibrium?
Thermal equilibrium is when there is no net flow of thermal energy (represented by temperature) through two systems.
In other words, objects with the same temperature are in thermal equilibrium.
117
What is the 0th law of thermodynamics?
If two systems A and B are both in thermal equilibrium with a system C, then A and B must be in thermal equilibrium with one another.
118
What happens to a heated object, and what happens to a cooled object? Why does this occur?
A heated object will expand, and a cooled object will contract.
When an object is heated, its molecules will have a greater kinetic energy and will overcome their attractions to one another, pushing apart and causing the object to expand. The reverse is true for cooling an object.
119
What is linear expansion, and how is it calculated?
Linear expansion is when a heated object expands in one dimension, and is given as
∆l= αl0∆T
Where
∆l is the change in length
α is the coefficient of linear expansion
l0 is the original length
∆T is the temperature change the object experiences
120
What is volume expansion, and how is it calculated?
Volume expansion is when a heated object expands in 3 dimensions, and is given as
∆V= βV0∆T
∆V is the change in volume
β is the coefficient of volume expansion
V0 is the original volume
∆T is the change in temperature
121
Why do liquids expand more than solids, and what is the exception to this?
Liquids expand more than solids as the bonds between their molecules are already much weaker than that of solids, and so the molecules are easier to pull apart.
Water is the exception to this, reducing in volume from 0 to 4 degress, and then expanding like normal
122
What causes thermal stress, and how is it calculated?
Thermal stress occurs when a heated object is prevented from expanding. The force of thermal stress is found by calculating how much the object should expand, and finding the force required to return the object to the original length. This reaction force is the force of thermal stress.
It is calculated from:
F/A = -Yα∆T
F = the stress force
A = cross sectional area
Y = Young's Modulus
α = coefficient of linear expansion
∆T = change in temperature (°C)
123
What is heat flow?
When energy is transfered from one object to another solely as a result of temperature difference.
