91Ó°ÊÓ

Problem 71

The mass of a flywheel is \(5.6 \times 10^{4} \mathrm{kg} .\) This particular flywheel has its mass concentrated at the rim of the wheel. If the radius of the wheel is \(2.6 \mathrm{m}\) and it is rotating at 350 rpm, what is the magnitude of its angular momentum?

Problem 72

The angular momentum of a spinning wheel is $240 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s} .$ After application of a constant braking torque for \(2.5 \mathrm{s}\), it slows and has a new angular momentum of $115 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s} .$ What is the torque applied?

Problem 73

How long would a braking torque of \(4.00 \mathrm{N}\).m have to act to just stop a spinning wheel that has an initial angular momentum of $6.40 \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s} ?$

Problem 74

A figure skater is spinning at a rate of 1.0 rev/s with her arms outstretched. She then draws her arms in to her chest, reducing her rotational inertia to \(67 \%\) of its original value. What is her new rate of rotation?

Problem 75

A skater is initially spinning at a rate of 10.0 rad/s with a rotational inertia of \(2.50 \mathrm{kg} \cdot \mathrm{m}^{2}\) when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to \(1.60 \mathrm{kg} \cdot \mathrm{m}^{2} ?\)

Problem 76

A uniform disk with a mass of \(800 \mathrm{g}\) and radius \(17.0 \mathrm{cm}\) is rotating on friction less bearings with an angular speed of \(18.0 \mathrm{Hz}\) when Jill drops a 120 -g clod of clay on a point \(8.00 \mathrm{cm}\) from the center of the disk, where it sticks. What is the new angular speed of the disk?

Problem 77

A spoked wheel with a radius of \(40.0 \mathrm{cm}\) and a mass of $2.00 \mathrm{kg}$ is mounted horizontally on friction less bearings. JiaJun puts his \(0.500-\mathrm{kg}\) guinea pig on the outer edge of the wheel. The guinea pig begins to run along the edge of the wheel with a speed of $20.0 \mathrm{cm} / \mathrm{s}$ with respect to the ground. What is the angular velocity of the wheel? Assume the spokes of the wheel have negligible mass.

Problem 78

A diver can change his rotational inertia by drawing his arms and legs close to his body in the tuck position. After he leaves the diving board (with some unknown angular velocity), he pulls himself into a ball as closely as possible and makes 2.00 complete rotations in \(1.33 \mathrm{s}\). If his rotational inertia decreases by a factor of 3.00 when he goes from the straight to the tuck position, what was his angular velocity when he left the diving board?

Problem 83

The Moon's distance from Earth varies between \(3.56 \times 10^{5} \mathrm{km}\) at perigee and \(4.07 \times 10^{5} \mathrm{km}\) at apogee. What is the ratio of its orbital speed around Earth at perigee to that at apogee?

Problem 84

A ceiling fan has four blades, each with a mass of \(0.35 \mathrm{kg}\) and a length of \(60 \mathrm{cm} .\) Model each blade as a rod connected to the fan axle at one end. When the fan is turned on, it takes 4.35 s for the fan to reach its final angular speed of 1.8 rev/s. What torque was applied to the fan by the motor? Ignore torque due to the air.