Rotational Motion

Question 1

What is meant by Torque (sometimes called the moment of a force)?

Answer 1

Torque is the turning effect of a force on a rotating object.

Question 2

What relationships would you use to convert between:

1. Linear displacement and angular displacement
2. Linear velocity and angular velocity
3. Linear acceleration and angular acceleration

Answer 2

For any of these relationships, you would multiply the angular quantity by the radius of circular motion to get the linear quantity:

Question 3

What does the prefix f stand for?

Answer 3

f = femto = x 10^-15

Question 4

How would you find the instantaneous velocity of an object from a displacement-time graph such as this?

Answer 4

Take the gradient of the line.

If the graph is a curve, take the gradient of the tangent to the curve at a point.

Question 5

Which two things does the moment of inertia of an object depend on?

Answer 5

1. The mass of the object
2. The distribution of mass around a given axis of rotation (which can be quantified with the radius, r)

Question 6

What does the prefix M stand for?

Answer 6

M = mega = x 10⁶

Question 7

What is the unit of angular displacement?

Answer 7

Radians (rad)

[note: rads is incorrect]

Question 8

What does the prefix G stand for?

Answer 8

G = giga = x 10⁹

Question 9

What does the prefix m stand for?

Answer 9

m = milli = x 10^-3

Question 10

How is angular acceleration defined in terms of angular velocity?

Answer 10

Angular acceleration is defined as the rate of change of angular velocity.

Question 11

What is the unit of moment of inertia?

Answer 11

kg m²

Question 12

What does the prefix p stand for?

Answer 12

p = pico = x 10^-12

Question 13

How is angular velocity defined in terms of angular displacement?

Answer 13

Angular velocity is defined as the rate of change of angular displacement:

Question 14

What is the unit of Torque?

Answer 14

newton-metres (Nm)

Question 15

What is the unit of angular acceleration?

Answer 15

rad s^-2

Question 16

What does the prefix k stand for?

Answer 16

k = kilo = x 10³

Question 17

What does the prefix P stand for?

Answer 17

P = peta = x 10¹⁵

Question 18

What is the unit of centripetal acceleration?

Answer 18

ms^-2

Question 19

What is the unit of angular velocity?

Answer 19

rad s^-1

Question 20

Convert 360° into radians.

Answer 20

360° = 2π radians = 6.28 rad

Question 21

The following experimental setup can be used to determine the moment of inertia of a disc which is allowed to rotate on a frictionless air bearing turntable.

Explain the measurements which will need to be taken, and how to use these to determine the moment of inertia of the disc.

Answer 21

Find the torque applied to the disc by using the relationship T = Fr.

Use the light gate to measure the angular acceleration of the disc.

Vary the hanging mass to vary the torque, and repeat a few times.

Plot T against α, and take the gradient of the straight line which will be equal to the moment of inertia of the disc.

Question 22

What is the definition of moment of inertia of an object?

Answer 22

The moment of inertia of an object is a measure of its resistance to angular acceleration about a given axis.

Question 23

How would you find the instantaneous acceleration of an object from a velocity-time graph such as this?

Answer 23

Take the gradient of the line.

If the graph is a curve, take the gradient of the tangent to the curve at a point.

Question 24

Which two quantities does the rotational kinetic energy of an object depend on?

Answer 24

Moment of Inertia and angular velocity

Question 25

What does the prefix T stand for?

Answer 25

T= tera = x 10¹²

Question 26

What is the unit of angular momentum?

Answer 26

kilogram metres squared per second

(kg m² s^-1)

(kg m² rad s^-1 also acceptable)

Question 27

Explain the difference between angular, tangential and centripetal acceleration.

Answer 27

• Angular acceleration is the rate of change of angular velocity
• Tangential acceleration is the rate of change of tangential speed
• Centripetal acceleration is the rate of change of tangential velocity- this causes the direction of the object to change and results in circular motion.

Question 28

What does the prefix µ stand for?

Answer 28

µ = micro = x 10^-6

Question 29

A ‘conical pendulum’ is shown below.

In terms of the components of tension in the string determine expressions for the:

1. Centripetal force
2. Weight of the ‘bob’.

Answer 29

1. Centripetal force = T sinθ
2. Weight = T cosθ

Question 30

In a ‘loop the loop’ ride at a funfair, how would you determine the minimum speed required to complete a full loop?

Answer 30

The minimum speed required is when there is no reaction force acting on the ‘car’, so.

Centripetal force = Weight + Reaction force

simplifies to

Centripetal force = Weight

mv²/r = mg

v = √gr

Question 31

An ice skater is spinning with his arms outward as shown.

He then pulls his arms inward.

Explain what happens to his angular momentum and rotational kinetic energy.

Answer 31

Angular momentum constant because angular momentum is always conserved

Rotational kinetic energy increases because angular velocity increases.

Question 32

What is the unit of tangential acceleration?

Answer 32

ms^-2

Question 33

A ball of weight W attached to a string is ‘whirling’ in a horizontal circle as shown below.

What provides the centripetal force acting on the ball?

Answer 33

The centripetal force is suppled by the tension, T only.

T is the only force acting into the centre.

Question 34

A ball of weight W attached to a string under tension T is ‘whirling’ in a vertical circle as shown below.

Determine a relationship for the centripetal force acting on the ball:

1. at the bottom.
2. at the sides.
3. at the top.

Answer 34

1. Centripetal force = Tension - Weight
2. Centripetal force = Tension
3. Centripetal force = Tension + Weight

Question 35

An expression for the displacement of an object with respect to time is given as

s = 3.1t² + 4.1t + 6

Determine expressions for the object’s velocity and acceleration.

Answer 35

v = 6.2t + 4.1

a = 6.2 (ms^-2)

Question 36

Describe how to convert an angular velocity in rpm (revolutions per minute) into rad s^-1 (radians per second).

Answer 36

revolutions per minute → radians per second:

× 2π then ÷ 60

Question 37

State the law of conservation of angular momentum.

Answer 37

In the absence of external torques, the total angular momentum of object(s) before a collision is equal to the total angular momentum of the object(s) after the collision.

Question 38

What does the prefix n stand for?

Answer 38

n = nano = x 10^-9

Question 39

Convert 15 revolutions into radians.

Answer 39

15 revolutions = 30π radians = 94.2 rad