Challenge Problems

121.

The angular acceleration of a rotating rigid body is given by $α = (2.0 - 3.0 t) rad / s^{2}$ . If the body starts rotating from rest at $t = 0$ , (a) what is the angular velocity? (b) Angular position? (c) What angle does it rotate through in 10 s? (d) Where does the vector perpendicular to the axis of rotation indicating $0 °$ at $t = 0$ lie at $t = 10 s$ ?

122.

Earth’s day has increased by 0.002 s in the last century. If this increase in Earth’s period is constant, how long will it take for Earth to come to rest?

123.

A disk of mass m, radius R, and area A has a surface mass density $σ = \frac{m r}{A R}$ (see the following figure). What is the moment of inertia of the disk about an axis through the center?

Figure shows a disk of radius r that rotates around an axis that passes through the center.

124.

Zorch, an archenemy of Rotation Man, decides to slow Earth’s rotation to once per 28.0 h by exerting an opposing force at and parallel to the equator. Rotation Man is not immediately concerned, because he knows Zorch can only exert a force of $4 .00 \times 1 0^{7} N$ (a little greater than a Saturn V rocket’s thrust). How long must Zorch push with this force to accomplish his goal? (This period gives Rotation Man time to devote to other villains.)

125.

A cord is wrapped around the rim of a solid cylinder of radius 0.25 m, and a constant force of 40 N is exerted on the cord shown, as shown in the following figure. The cylinder is mounted on frictionless bearings, and its moment of inertia is $6.0 kg \cdot m^{2}$ . (a) Use the work energy theorem to calculate the angular velocity of the cylinder after 5.0 m of cord have been removed. (b) If the 40-N force is replaced by a 40-N weight, what is the angular velocity of the cylinder after 5.0 m of cord have unwound?

Figure shows a cord that is wrapped around the rim of a solid cylinder. A constant force of 40 N is exerted on the cord. Figure shows a cord that is wrapped around the rim of a solid cylinder. A 40 N weight is connected to the cord and hangs in air.