91Ó°ÊÓ

Problem 1

Verify that \(\frac{1}{2} I \omega^{2}\) has dimensions of energy.

Problem 2

What is the rotational inertia of a solid iron disk of mass \(49 \mathrm{kg},\) with a thickness of \(5.00 \mathrm{cm}\) and radius of \(20.0 \mathrm{cm}\) about an axis through its center and perpendicular to it?

Problem 3

A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is the (a) mass and (b) rotational inertia of the child's ball reduced compared with the adult ball?

Problem 6

How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of \(12.0 \mathrm{cm}\) and a mass of \(15.8 \mathrm{g} .\) The laser scans at a constant tangential velocity of \(1.20 \mathrm{m} / \mathrm{s} .\) Assume that the music is first detected at a radius of \(20.0 \mathrm{mm}\) from the center of the disk. Ignore the small circular hole at the CD's center.

Problem 8

A bicycle has wheels of radius \(0.32 \mathrm{m}\). Each wheel has a rotational inertia of \(0.080 \mathrm{kg} \cdot \mathrm{m}^{2}\) about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels?

Problem 9

In many problems in previous chapters, cars and other objects that roll on wheels were considered to act as if they were sliding without friction. (a) Can the same assumption be made for a wheel rolling by itself? Explain your answer. (b) If a moving car of total mass \(1300 \mathrm{kg}\) has four wheels, each with rotational inertia of \(0.705 \mathrm{kg} \cdot \mathrm{m}^{2}\) and radius of \(35 \mathrm{cm},\) what fraction of the total kinetic energy is rotational?

Problem 10

A centrifuge has a rotational inertia of $6.5 \times 10^{-3} \mathrm{kg} \cdot \mathrm{m}^{2}$ How much energy must be supplied to bring it from rest to 420 rad/s \((4000 \text { rpm }) ?\)

Problem 11

A mechanic turns a wrench using a force of \(25 \mathrm{N}\) at a distance of \(16 \mathrm{cm}\) from the rotation axis. The force is perpendicular to the wrench handle. What magnitude torque does she apply to the wrench?

Problem 12

The pull cord of a lawnmower engine is wound around a drum of radius $6.00 \mathrm{cm} .\( While the cord is pulled with a force of \)75 \mathrm{N}$ to start the engine, what magnitude torque does the cord apply to the drum?

Problem 13

A child of mass \(40.0 \mathrm{kg}\) is sitting on a horizontal seesaw at a distance of \(2.0 \mathrm{m}\) from the supporting axis. What is the magnitude of the torque about the axis due to the weight of the child?