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

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

What relationships would you use to convert between:

- Linear displacement and angular displacement
- Linear velocity and angular velocity
- Linear acceleration and angular acceleration

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

What does the prefix **f** stand for?

**f** = femto = **x 10 ^{-15}**

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

Take the **gradient** of the line.

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

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

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

What does the prefix **M** stand for?

**M** = mega = **x 10 ^{6}**

What is the unit of angular displacement?

Radians (rad)

**[note:** *rads***is incorrect]**

What does the prefix **G** stand for?

**G** = giga = **x 10 ^{9}**

What does the prefix **m** stand for?

**m** = milli = **x 10 ^{-3}**

How is angular acceleration defined in terms of angular velocity?

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

What is the unit of moment of inertia?

**kg m ^{2}**

What does the prefix **p** stand for?

**p** = pico = **x 10 ^{-12}**

How is angular velocity defined in terms of angular displacement?

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

What is the unit of Torque?

**newton-metres (Nm)**

What is the unit of angular acceleration?

**rad s ^{-2}**

What does the prefix **k** stand for?

**k** = kilo = **x 10 ^{3}**

What does the prefix **P** stand for?

**P** = peta = **x 10 ^{15}**

What is the unit of centripetal acceleration?

**ms ^{-2}**

What is the unit of angular velocity?

rad s^{-1}

**Convert 360° into radians.**

360° **= 2π radians = 6.28 rad**

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.

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.

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

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

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

Take the **gradient** of the line.

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

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

**Moment of Inertia** and **angular velocity**

What does the prefix **T** stand for?

**T**= tera = **x 10 ^{12}**

What is the unit of angular momentum?

kilogram metres squared per second

(kg m^{2} s^{-1})

(kg m^{2} rad s^{-1 }also acceptable)

Explain the difference between angular, tangential and centripetal acceleration.

- 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.

What does the prefix **µ** stand for?

**µ** = micro = **x 10 ^{-6}**

A ‘conical pendulum’ is shown below.

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

- Centripetal force
- Weight of the ‘bob’.

- Centripetal force = T sinθ
- Weight = T cosθ

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

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

mv^{2}/r = mg

**v = √gr**

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.

Angular momentum **constant** because angular momentum is always conserved

Rotational kinetic energy **increases** because angular velocity increases.

What is the unit of tangential acceleration?

**ms ^{-2}**

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?

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

T is the only force acting into the centre.

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:

- at the bottom.
- at the sides.
- at the top.

- Centripetal force = Tension - Weight
- Centripetal force = Tension
- Centripetal force = Tension + Weight

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

s = 3.1t^{2} + 4.1t + 6

Determine expressions for the object’s velocity and acceleration.

**v = 6.2t + 4.1**

**a = 6.2 (ms ^{-2})**

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

revolutions per minute → radians per second:

**× 2π** then **÷ 60**

State the law of conservation of angular momentum.

**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.

What does the prefix **n** stand for?

**n** = nano = **x 10 ^{-9}**

Convert 15 revolutions **into radians**.

15 revolutions **= 30π radians = 94.2 rad**