5. A solid sphere of radius r = 34.5 cm and mass m = 1.80 kg starts from rest and rolls without slipping down a 30° incline that is 10.0 m long. a) Find the translational and rotational speeds when it reaches the bottom. b) Find the ratio of the rotational kinetic energy to the translational kinetic energy without using any numbers. What do you notice?

A disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed i. A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (Fig. P10.50). Because of friction between the surfaces, the two eventually reach the same angular speed f. (a) Calculate f. (b) Calculate the ratio of the final to the initial rotational energy. Figure P10.50

A system consists of a disk of mass 2.0 kg and radius 50 cm upon which is mounted an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm (see below). The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s. (a) What is the moment of inertia of the system? (b) What is its rotational kinetic energy?

An electric sander consisting of a rotating disk of mass 0.7 kg and radius 10 cm rotates at 15 rev/sec. When applied to a rough wooden wall the rotation rate decreases by 20 . (a) What is the final rotational kinetic energy of the rotating disk? (a) How much has its rotational kinetic energy decreased?

Calculate the rotational kinetic energy of a 12-kg motorcycle wheel if its angular velocity is 120 rad/s and its inner radius is 0.280 m and outer radius 0.330 m.

Suppose a child gets off a rotating merry-go-round, Does the angular velocity of the merry-go-round increase, decrease, or remain the same if: (a) He jumps off radially? (b) He Jumps backward to land motionless? (c) He jumps straight up and hangs onto an overhead tree branch? (d) He jumps off forward, tangential to the edge? Explain your answers. (Refer to Figure 10.34).

A diver goes into a somersault during a dive by tucking her limbs. If her rotational kindetic energy is 100 J and her moment of inertia in the tuck is 9.0kgm2 , what is her rotational rate during the somersault?

A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different moments, its angular speed is 2 rad/s, 0. and +2 rad/s. For a point on the rim of the wheel, consider at these moments the magnitude of the tangential component of acceleration and the magnitude of the radial component of acceleration. Rank the following five items from largest to smallest: (a) |at| when = 2 rad/s, (b)|ar| when = 2 rad/s, (c)|ar| when = 0, (d) |at| when = 2 rad/s, and (e) |ar| when = 2 rad/s. If two items are equal, show them as equal in your ranking. If a quantity is equal to zero, show that fact in your ranking.

Repeat Example 10.15 in which the stick is free to have translational motion as well as rotational motion.

Consider the 12.0 kg motorcycle wheel shown in Figure 10.38. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s? Figure 10.38 A motorcycle wheel has a moment of inertia approximately