Engineering Physics- PART 2 Flashcards
(86 cards)
1
Q
What newton’s Second Law for Rotation?
A
In linear motion, the force required to give an object a certain acceleration depends on its mass
[GIVEN]
2
Q
In rotational motion, what does the torque required to give a rotating object a certain angular acceleration depend on?
A
it depends on its moment of inertia
[GIVEN]
3
Q
Draw a circle with Newton’s second law
A
Newton’s second law for rotating bodies is equivalent to Newton’s second law for linear motion
4
Q
Where does Newton’s Second Law of rotational motion equation come from?
A
5
Q
How can the moment of inertia of a rotating body can be thought of?
A
as analogous to (the same as) mass
- The inertia of a mass describes its ability to resist changes to linear motion, which is referring to linear acceleration
- Similarly, the moment of inertia of a mass describes its ability to resist changes to rotational motion, which is referring to angular acceleration
6
Q
What is the formula for angular acceleration and moment of inertia?
A
[ONLY SECOND ONE GIVEN]
7
Q
What is the formula for angular acceleration and moment of inertia with the equations for force and torque?
A
[ONLY LAST ON IS GIVEN]
8
Q
Draw a table to compare linear and rotational variables in Newton’s Second Law
A
9
Q
What is angular momentum?
A
Angular momentum is the rotational equivalent of linear momentum
10
Q
What is the formula for angular momentum?
A
defined by mass × velocity, or
[GIVEN]
11
Q
Draw a diagram of angular momentum?
A
The angular momentum of a rotating wheel is the product of the moment of inertia and angular velocity of the wheel
12
Q
The moment of inertia of a rotating point mass m which is a distance r from an axis of rotation is equal to what?
A
[GIVEN]
13
Q
What is the angular velocity of the point mass?
A
[NOT GIVEN]
14
Q
What is the angular momentum of the point mass?
A
15
Q
A
16
Q
Tip!!
A
You should know that objects travelling in straight lines can have angular momentum - just make sure you understand that it all depends on the position of the object in relation to the axis of rotation being considered
17
Q
Is angular momentum conserved?
A
As with linear momentum, angular momentum is always conserved
18
Q
How does the principle of conservation of angular momentum conservation law have many real-world applications?
A
- A person on a spinning chair spins faster while their arms and legs are contracted and slower while extended
- Objects in elliptical orbits travel faster nearer the object they orbit and slower when further away
- Ice skaters can change their rotational velocity by extending or contracting their arms
-Tornados spin faster as their radius decreases
18
Q
What is the principle of conservation of angular momentum states?
A
The angular momentum of a system always remains constant, unless a net torque is acting on the system
19
Q
Describe how Ice skaters can change their moment of inertia
A
Ice skaters can change their moment of inertia by extending or contracting their arms and legs. Due to the conservation of angular momentum, this allows them to spin faster or slower
20
Q
How can problems involving a change in angular momentum can be solved?
A
[original equation given]
21
Q
In linear motion, how can the resultant force on a body be defined?
A
the resultant force on a body can be defined as the rate of change of linear momentum
[NOT GIVEN]
22
Q
Define linear impulse?
A
[GIVEN]
23
Q
Define the resultant torque on a body?
A
the rate of change of angular momentum
24
What is the equation for resultant torque?
[not given]
25
Define angular impulse, and give the equation
[GIVEN]
26
What is angular impulse measured in?
kg m^2 s^−1
or N m s
27
What doe the angular impulse equation require?
requires the use of a constant resultant torque
If the resultant torque changes, then an average of the values must be used
28
What is the difference between a small or large torque?
Angular impulse describes the effect of a torque acting over a time interval
This means a small torque acting over a long time has the same effect as a large torque acting over a short time
29
What is the area under a torque-time graph equal to?
The area under a torque-time graph is equal to the angular impulse or the change in angular momentum
- This is because the area, angular impulse, is a fraction of the base × height, torque × time, ΔL = τΔt
-The fraction of torque × time depends upon the shape of the area under the graph
30
What does the Torque-Time Graph look like?
When the torque is not constant, the angular impulse is the area under a torque-time graph
31
TIPPP!
Many applications for angular impulse will be related to sports. These are similar to the linear impulse topic
32
What has to happen when a torque turns in through an angle about an axis?
Work has to be done on a rigid body when a torque turns in through an angle about an axis
For example, rotating cranes and fairground rides
33
the work done for a rotating object is defined by the equation...
In systems with linear acceleration, work W is the product of the force and the distance moved
[GIVEN]
34
What is another way work can be calculated?
by finding the area under a torque-angular displacement graph
35
What does a Torque-angular displacement graph look like?
36
What is the area under the torque-angular displacement graph?
the work done
This is analogous to the work done being the area under a force-displacement graph
37
Define Power
Power is the rate of doing work
38
What is the formula for power?
[middle and last GIVEN]
39
TIPP!
Don't forget that θ is always in radians when you're doing conversions from revs s–1 or rev min–1.
40
In rotational mechanics, what do frictional forces produce?
In rotational mechanics, frictional forces produce a specific torque called frictional torque
This is the torque caused by the frictional force when two objects in contact move past each other
41
Define frictional torque
The difference between the applied torque and the resulting net, or observed, torque
This means that the net torque is the sum of the applied and frictional torque
Net torque = applied torque + frictional torque
[NOT GIVEN]
42
In rotating machinery, why does the power have to be expended to overcome frictional torque?
This is due to resistive forces within the machinery
43
Why is frictional torque is minimised?
to reduce the kinetic energy losses transferred to heat and sound
However, sometimes a frictional torque is applied, such as when using a screwdriver
When a screwdriver is gripped and turned, this increases its rotational kinetic energy
44
What must the fictional forces always do?
The frictional force must always be added to the torque resulting from a force to get the total torque in the system
45
Frictional torque is calculated using the same equations as torque...
[GIVEN SEPEATLY]
46
A body moving with linear velocity has an associated linear kinetic energy given by what equation?
[First GIVEN, last GIVEN]
47
Similarly, a rotating body with angular velocity has an associated rotational kinetic energy given by...
[FIRST GIVEN ONLY]
48
So, what happens when a disc rolls without slipping?
- There is enough friction present to initiate rotational motion allowing the object to roll
- The point in contact with the surface has a velocity of zero
- The centre of mass has a velocity of v = wr
- The top point has a velocity of or 2v or 2wr
48
How are circular object made to move?
Circular objects, such as wheels, are made to move with both linear and rotational motion
For example, the wheels of a car, or bicycle rotate causing it to move forward
Rolling motion without slipping is a combination of rotating and sliding (translational) motion
48
What happens when a disc slips or slides?
- There is not enough friction present to allow the object to roll
- Each point on the object has the same linear velocity
- The angular velocity is zero
49
What happens when a disc rotates?
- Each point on the disc has a different linear velocity depending on its distance from the centre
- The linear velocity is the same at all points on the circumference
50
Draw an image of rotation and translation?
Rolling motion is a combination of rotational and translational motion. The resultant velocity at the bottom is zero and the resultant velocity at the top is 2v
51
Describe, another common scenario involving rotational and translational motion
an object (usually a ball or a disc) rolling down a slope
[GIVEN]
52
Draw an image of this ball?
The GPE store of the ball is transferred to the translational and rotational kinetic energy store as it rolls down the slope
53
How can the linear or angular velocity be determined?
[GIVEN]
54
Give an example of how the linear or angular velocity be determined?
55
TIP!!!!
Questions with a long calculation like this are best to split sections when putting them into your calculator. This makes it easier to check and type, ensuring the brackets are in the correct place. It is best to type it in exactly as you have it written down so it is input correctly.
The question asks for the magnitude of the change in rotational kinetic energy. If you found the KE after − KE after then the answer is negative. No worries because the change is the same, no matter which way you find the difference,
Looking at the angular velocity before and after, when it is smaller, tells us that the rotational kinetic energy will also be less.
56
Why are flywheels used in machines?
Flywheels are used in machines to act as an energy reservoir, by storing and supplying energy when required
57
What are flywheels made from?
They consist of a heavy metal disc or wheel that can rotate rapidly and so has a large moment of inertia
This means it has:
1. a high mass
2. a large radius
This means once they start spinning, it is difficult to make them stop
58
Give an example of a flywheel in machines
An example is a treadle (pedal) sewing machine
- This consists of a big flywheel, connected to a small wheel by a rope which drives the sewing machine
- A pedal is pressed which causes the flywheel to rotate, and also rotates the smaller wheel which drives the machine
- When the pedal is not pressed, the smaller wheel will still rotate for some time due to the energy stored in the flywheel
- This is because the flywheel has stored the rotational energy, which it can now transfer for some time after there is no input. This is used extensively in machines to control energy transfers
59
Where are flywheels primarily used?
Flywheels are primarily used in engines in vehicles where they accumulate and store energy
60
What happens in a flywheel?
[I = mr^2 is given].........
60
Draw a a uniform solid disc and a spoked wheel (both flywheel shapes)
Neglecting the mass of the spokes and axle, a disc-shaped flywheel has a smaller moment of inertia than a wheel-shaped one
61
Where are these flywheels often found?
These flywheels were often fitted in large Victorian steam engines used in pumping stations and textile mills
They had a huge rim fitted with spokes
This gave a greater moment of inertia than if the same mass had been used to create a solid disc flywheel of the same diameter
62
Describe how a flywheel overcomes friction?
A flywheel transfers just enough power to a wheel to overcome frictional torque as it rotates
When power is needed to the rest of the engine, the flywheel can reduce its speed and transfer some power
63
TIPS!
Questions about flywheels involve calculating torque and moments of inertia, so make sure you're confident with these calculations. Flywheels are just one common application of torque and moment of inertia
64
What are flywheel used for?
1) Smooth out fluctuations in rotational speed / torque / power (such as in vehicles)
2) Store rotational kinetic energy
65
Describe how power in an engine is produced?
Power in an engine is not produced continuously, only in the 'power stroke' or 'combustion' part of an engine cycle, so it is released in bursts
This causes an engine to produce a torque that fluctuates
66
What does a torque do to a flywheel?
- The torque makes the flywheel rotate, moving a vehicle forwards
- If the torque is uneven, it will cause a jerky motion and unwanted vibrations will occur. This is a waste of energy and uncomfortable for the passengers
- The flywheel added will speed up or slow down over a period of time because of its inertia and as a result, the sharp fluctuations in torque are 'smoothed'
67
Draw a flywheel in a four-cylinder engine
Flywheels smooth out the rotation of a crankshaft in a four-cylinder car
68
What happens the greater the moment of inertia of the flywheel?
the smaller the fluctuation in speed
69
What happens in conventional breaking?
In conventional braking (say, on a bike), the kinetic energy store of the vehicle is transferred as waste through to the thermal energy store
70
Instead, what happens when regenerative brakes are applied?
a flywheel is engaged and will 'charge up' by using the energy lost by braking
When the vehicle needs to accelerate later, the energy stored by the flywheel is used to do this
These systems are sometimes called 'KERS' (kinetic energy recovery systems)
71
Draw a diagram of a regenerative braking system
72
How does a regenerative braking system use a flywheel?
A regenerative braking system uses a flywheel which charges up from the energy lost by braking
73
How can an electric motor in industrial machines can be used along with a flywheel?
- The motor is used to charge up the flywheel, which can then transfer short burst of energy (such as needing to connect two materials together in a riveting machine)
- This prevents the motor from stalling, and a less powerful motor can be used
74
What factors affect the energy storage capacity?
1) the mass of the flywheel
2) the angular speed of the flywheel
3) Friction
4) the shape of the flywheel
75
How does the mass of the flywheel affect the energy storage capacity?
- Since the moment of inertia, I is directly proportional to the mass, m, as mass increases the moment of inertia also increases
- The rotational kinetic energy is directly proportional to the moment of inertia, so this also increases
76
How does the angular speed of the flywheel affect the energy storage capacity?
- The rotational kinetic energy is proportional to the square of the angular speed
- If the angular speed increases, the rotational kinetic energy stored also increases
77
How does the Fiction affect the energy storage capacity?
Although they are very efficient, flywheels can still lose some stored energy as friction and air resistance between the wheels and its bearings
78
How can the friction be reduced?
1) Lubricating bearings
2) Using bearings made of superconductors, so the flywheel can levitate and have no contact
3) Use the flywheel in a vacuum or sealed container to reduce air resistance
79
The shape of the flywheel, for a solid disc of radius R, thickness t, mass M and density, what is the equation?
[NOT GIVEN]
80
What is the moment of inertia about the axis of rotation for a disc?
[NOT GIVEN]
81
So what is the rotational kinetic energy equation?
[ONLY FIRST EQUATION GIVEN]
82
TIPP!
A question might ask about the function of a flywheel, or an application. These are two different things.
The function is why we use a flywheel - this is to store rotational kinetic energy. An application might be degenerative braking
