# Worksheet: Angular Impulse

In this worksheet, we will practice calculating the angular impulse given to an object when a torque is applied to it for a period of time.

**Q1: **

Which of the following quantities has the same units as angular impulse?

- AMoment of inertia
- BTorque
- CLinear momentum
- DAngular velocity
- EAngular momentum

**Q2: **

An object is rotating with an angular velocity of 44 rad/s. A torque of 0.23 N⋅m is applied to the object, which brings it to a stop in 135 s. What is the moment of inertia of the object? Give your answer to 2 significant figures.

**Q3: **

An object with a moment of inertia of 3.2 kg⋅m^{2}
around its axis of rotation initially has an angular velocity of
5.0 rad/s.
A torque is applied to the object for 22 s,
after which time it has an angular velocity of 48 rad/s.
What is the magnitude of the torque applied to the object? Give your answer to 2 significant figures.

**Q4: **

The wheel of a truck has a moment of inertia around its axis of rotation of
5.8 kg⋅m^{2}.
The wheel is initially rotating at
52 rad/s.
The brakes of the truck can apply a maximum torque of
24 kg⋅m^{2}/s^{2}
to the wheel. What is the minimum time in which the brakes of the truck can be used to stop the
wheels from turning? Give your answer to 3 significant figures.

- A 139 s
- B 215 s
- C 0.370 s
- D 2.68 s
- E 12.6 s

**Q5: **

A torque of 3.4 nm
is applied to a solid metal disk over a period of time,
giving the disk an angular impulse of 187 kg⋅m^{2}/s. For how long was the torque applied to the disk?

**Q6: **

The wheel of a bike that is initially not rotating has a moment of inertia around its axis of rotation of
0.800 kg⋅m^{2}. A torque of 0.450 nm
is applied to the wheel for 12.0 s.
What is the magnitude of the angular velocity of the wheel at the end of this time?

**Q7: **

An object is given an angular impulse of 16 kg⋅m^{2}/s over
64 s. What average torque was applied to the object?

**Q8: **

An ice-skater performs a spin on an ice rink.
At the start of the spin, he gains an angular impulse of
450 kg⋅m^{2}/s in just
0.60 s.
What average torque was applied to the ice-skater over this time?

**Q9: **

A washing machine applies a torque of
8.0 kg⋅m^{2}/s^{2}
to the drum of the machine over a period of time,
giving the drum an angular impulse of
960 kg⋅m^{2}/s.
For how long was the torque applied to the drum?

**Q10: **

A torque of 0.2 kg⋅m^{2}/s^{2} is applied to an object for
20 s.
Then, a torque of
0.5 kg⋅m^{2}/s^{2}
is applied to the object for 5 s.
What is the total angular impulse given to the object? Give your answer to two significant figures.

**Q11: **

The SI units of torque are kilogram meters per second squared
(kg⋅m^{2}/s^{2}).
If a torque is multiplied by a time, what are the SI units of the resultant quantity?

- A
kg⋅m
^{2}⋅s - B
kg⋅m
^{2} - C
kg⋅m
^{2}/s^{3} - D
kg⋅m
^{2}⋅s^{2} - E
kg⋅m
^{2}/s

**Q12: **

A car accelerates for 20 s, during which time a torque of 32 N⋅m is applied to each of the wheels. What angular impulse was given to each wheel over the time it accelerates for?

**Q13: **

The graph shows the torque that is applied to an object over time.

What is the average torque applied between 0 and 4 seconds?

What angular impulse is given to the object between 0 and 4 seconds?

**Q14: **

The graph shows the torque applied to the rear wheel of a bike over time. What angular impulse is given to the wheel between 0 s and 7 s?