Rotational Inertia

if the same torque is applied on a hoop (I=MR²) and a solid disk (I=1/2MR²), after 5s which object will be moving faster?

• Hoop

• Solid Disk

The object with more rotational inertia needs more torque to move than object with lower inertia?

• True

• False

what is the angular acceleration of an object that has rotational inertia of 4 kg.m² and submitted to a torque of 8 N.m?

• 0.5 rad/s²

• 2 rad/s²

• 4 rad/s²

• 8 rad/s²

If the torque required to loosen a nut on the wheel of a car has a magnitude of 60.0 N• m, what minimum perpendicular force must be exerted by a mechanic at the end of a 45.0 cm wrench to loosen the nut?

• 0.666 Nm
•  133.3 N
• 66.7 N
• 13.3 Nm

Where should another 4 N force be applied to maximize the net torque on the object?

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A figure skater spins on an icy surface. Her moment of inertia is 3.0 kg-m² when her arms are stretched away from her and drops to 2.2 kg-m² when her arms are close to her chest. If she makes three revolutions per second (rps) when her arms are stretched, how many rps will she make when she puts her arms to her chest?

Hint: You will need to use conservation of Angular Momentum!

• 4 rps

• 2 rps

• 3 rps

• 8 rps

Rotational Inertia

We know that to change an object’s linear velocity requires a force.

Likewise to change an object’s angular velocity requires a torque.

Mass, or inertia means “how hard it is to change the velocity of an object”.

The rotational equivalent of mass is rotational inertia.

It means “how hard it is to change the _______ ________ of an object”.

Explain why a ring is harder to spin than a solid disc (of same mass and radius)

• the ring has its mass further from the center (on average)

• the solid disc has its mass further from the center (on average)

• The ring has a smaller rotational inertia

• The ring has a larger rotational inertia

A bike wheel with a rotational inertia of 0.23 kgm² is initially moving with ω = 34 rads^-1. A force of 5.0 N is applied at 0.55 m from the centre of rotation until the wheel is brought to rest. What is the size of the angular acceleration and how long does it take to stop?

• α = 12 rads^-2 and t = 2.8 s

• α = 2.9 rads^-2 and t = 2.9 s

• α = 16 rads^-2 and t = 5.0 s