# 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⋅m2 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⋅m2. The wheel is initially rotating at 52 rad/s. The brakes of the truck can apply a maximum torque of 24 kg⋅m2/s2 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⋅m2/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⋅m2. 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⋅m2/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⋅m2/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⋅m2/s2 to the drum of the machine over a period of time, giving the drum an angular impulse of 960 kg⋅m2/s. For how long was the torque applied to the drum?

Q10:

A torque of 0.2 kg⋅m2/s2 is applied to an object for 20 s. Then, a torque of 0.5 kg⋅m2/s2 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⋅m2/s2). If a torque is multiplied by a time, what are the SI units of the resultant quantity?

• A kg⋅m2⋅s
• B kg⋅m2
• C kg⋅m2/s3
• D kg⋅m2⋅s2
• E kg⋅m2/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?