Mechanics

Question 1

Newton’s First Law

Answer 1

Law of Inertia:
An object remains in its current state of motion until an external force is exerted on said object.

Question 2

Newton’s Second Law

Answer 2

Law of Forces:
An objects acceleration (change in motion) is dependent on the mass of the object and the amount of force applied

F = ma

Question 3

Newton’s Third Law

Answer 3

Law of Action & Reaction:
When one object exerts a force on a second object. The second object exerts an equal and opposite force on the first.

Question 4

Newton’s Law of Gravitation

Answer 4

Any mass in the universe attracts to another with a force varying directly as the product of the masses and inversely square to the distance between them.

F = GMm / r^2

Question 5

Gravitational Potential Energy

Answer 5

Is the energy required to take one mass from infinity to the the seperation distance between the objects.

U = -GMm / r

Question 6

1. Why is gravitational potential energy negative.
2. what is the zero point?

Answer 6

1. It’s equivalent to gravity working to move from a mass out to infinity. When gravity is doing work, the sign is negative.
2. At infinity, gravitational potential energy is zero, it’s losing potential energy and gaining kinetic energy.

Question 7

1. Why is U (close to Earth) always positive?
2. Why is g fixed?

Answer 7

1. The sign of change in potential energy does not matter.
2. The change in g over a small distance is very small, that a change in g is ignored.

Question 8

Escape Velocity

Answer 8

The minimum velocity an object needs to leave a gravitational body so to be able to reach infinity.
1. Conservation of energy between surface of gravitational body to infinity is analysed.
2. At infinity the object’s velocity and kinetic energy is zero.

Question 9

Orbital Velocity

Answer 9

The average speed of an object orbiting a gravitational mass that is required to,
1. Counter the effect of gravity.
2. Not be able to escape the orbit.

-

Question 10

Force and Potential Energy function

Answer 10

A conservative force is opposite (including direction) to the change in potential energy with respect to displacement.

F = -dU / dx

Question 11

1. Stable Equilibrium
2. Unstable Equilibrium

Answer 11

1. Movement away from the equilibrium pt results in a force back towards the equilibrium pt. (local min)
2. Movement away from equilibrium pt results in a force away from equilibrium pt to a lower potential energy (local max)

Question 12

Total energy

Answer 12

E = K + U

Question 13

Angular Momentum

Answer 13

How much an object will continue to rotate without an applied external torque.
If conserved both r and direction are conserved.

L = r x p = mr x v = rpsin(theta)

When r and p are perpendicular, L is at maximum and zero when parallel.

Question 14

Torque

Answer 14

Represents a change in angular momentum of a rotating object. Is an external force exerting on a rotating object.

† = r x F = r x dL / dt

Question 15

Projection Method

Answer 15

Useful for evaluating angular momentum magnitude or any cross product.

Can explain how the magnitude of the cross product of two vectors is equal to the product of the magnitude of the other vectors.

Question 16

Kepler’s First law

Answer 16

Law of Ellipses:

The path of the planets around the sun is elliptical in shape, with the sun being located at one focus.

1. Hyperbola = e > 1 = E > 0
2. Parabola = e = 1 = E = 0
3. Ellipse = 0 < e < 1 = E < 0
4. Circle = e = 0 = E < 0

Question 17

Kepler’s Second Law

Answer 17

Law of Equal areas:

An imaginary line drawn from the sun to the planet will sweep out equal areas in equal intervals of time.

Explains how angular momentum is conserved in the case of a central force. Thus the magnitude and direction is constant.

Question 18

Kepler’s Third Law

Answer 18

Law of Harmonics:

The square of the orbital period of any planet is proportional to the cube of the semi major axis of the elliptical orbit.

Question 19

What happens when
1. E < 0
2. E ≥ 0

Answer 19

1. Object is in orbit, trapped in a potential well.
2. Object has sufficient K that prevents it from being trapped in the potential well.

Question 20

What is the total energy of a particle in a circular gravitational orbit?

Answer 20

1. E = K + U
2. E = GMm/2r - GMm/r
3. E = -GMm/2r
4. E = U/2
   - For a particle in a circular orbit the total energy is negative and half of the gravitational potential energy.

Question 21

What is the total energy in a stable orbital motion?

Answer 21

E = 1/2m[v^2(rad) +v^2(per] + U(r)

E = m/2(dr/dt)^2 + Ueff

Where v(per) = L / mr
and v(rad) = dr / dt

Question 22

1. What is effective potential for radial motion?
2. What does the derivative of this mean?

Answer 22

1. Ueff = L^2/2mr^2 + U(r). Is only concerned with the magnitude of r.
2. Gives the effective radial force. That only changes the magnitude of r.

Question 23

Effective vs True Force at 0

Answer 23

1. Effective force is zero, will result in a circular orbit.
2. True force is zero. The motion will be zero.

Question 24

Why do we need Moment of Inertia?

Answer 24

Explains how the mass is distributed throughout the object on a rotating axis.
Due to the varying speeds due to the varying radius.

Question 25

1. Explain rot discrete masses 2. Explain rot continuously distributed masses

Answer 25

1. I = sum(m(i)r^2(i)) Describes the perpendicular radius from a point of mass. 2. I = Int(r^2dm) Sums all the mass over a given volume. dm = density * dV

Question 26

Centre of Mass for: 1. Discrete Masses 2. Continuous body of masses

Answer 26

1. R = M^-1 [sum(r(i)m(i)] 2. R = M^-1[int(rdm)] limits are defined by the volume.

Question 27

Parallel axis theorum

Answer 27

I = I(R) + MD^2 Occurs when we set the rotational axis away from the centre of mass.

Question 28

Perpendicular Axis Theorum

Answer 28

I(z) = I(x) + I(y) Useful when finding I on a specific axis for a planner object.

Question 29

Elastic Collisions

Answer 29

a. Objects seperate on impact. b. Momentum conserved (net external force is zero) c. Perfect collisions, kinetic energy is conserved. d. Imperfect collisions, kinetic energy is lost.

Question 30

Inelastic collisions

Answer 30

a. Momentum is conserved. b. Kinetic energy is not conserved. c. Perfect collisions, max kinetic energy is lost and objects stuck together. d. Imperfect collisions, some kinetic energy lost, objects not technically stuck together.

Question 31

Referance Frame

Answer 31

An co-ordinate system which is visualised as an imaginary lattice of axis perpendicular to each other in 3D space.

Question 32

Inertial Referance Frame and 1. The two postulates. 2. Transformations.

Answer 32

Reference frame that has no change in motion. 1a. The laws of physics are the same in all inertial frames. 1b. The basic laws are unchanged when referance frames are transformed. 2. t' = t y' = y z' = z x' = x - Vt x = x' + Vt a = a'

Question 33

Centre of Momentum Frame

Answer 33

The total momentum of the system is zero. p'1 = p'2, p'1 = -p'2 Both equations obey momentum and energy conservation. The sign indicates the direction they travelling on axis. v'1 = -w'1 and v'2 = -w'2

Question 34

Centre of Mass frame

Answer 34

Same as centre of momentum except reference frame is at centre of mass.

Question 35

Non-inertial Reference Frames

Answer 35

Reference frames that are accelerating x = x' + x0 v = v' + v0 a = a' + a0 F' = F + ma0 An inertial observer will see things fly off in a tangential velocity. A non-inertial observer will observe an acceleration (not a real acceleration)

Question 36

Rotating Frames: Centrifugal Force

Answer 36

A ficticious force that is an apparant outward force holding a mass in place, but in an inertial frame is moving in a circle. Is dependent on rotating frames radius. F = -mw x (w x r)

Question 37

Rotating Frames: Corriolus force

Answer 37

A ficticious force that makes a radial path in an inertial frame of reference act as a curved path in a rotating frame. Is dependent on objects velocity in the rotating frame. F = -2mw x v