Page 139 - Schaum's Outline of Theory and Problems of Applied Physics

124 ROTATIONAL MOTION [CHAP. 10

(c) A and B reach the bottom together.
(d) Any of the above, depending on the angle of the ramp.

10.12. When the cylinders of Question 10.11 reach the bottom of the ramp,
(a) the KE of A is more than the KE of B
(b) the KE of B is more than the KE of A
(c) A and B have the same KE
(d) any of the above, depending on the angle of the ramp

10.13. A solid wooden disk rolls down a ramp. The center of the disk is then cut out, and the resulting doughnut rolls down
the same ramp. At the bottom of the ramp the doughnut’s velocity is
(a) less than that of the solid disk
(b) the same as that of the solid disk
(c) greater than that of the solid disk
(d) any of the above, depending on the angle of the ramp
2
10.14. A flywheel whose moment of inertia is 4.0 kg·m is acted on by a torque of 50 N·m. Six seconds after starting from
an angular velocity of 40 rad/s the flywheel will have turned through
(a) 225 rad (c) 465 rad
(b) 315 rad (d) 3053 rad

10.15. The KE of the flywheel of Question 10.14 will have increased by
(a) 8.05 kJ (c) 23.25 kJ
(b) 11.25 kJ (d) 26.45 kJ

2
10.16. The torque needed to bring a turbine whose moment of inertia is 60 slug·ft to rest in 12 s from an initial angular
velocity of 80 rad/s is
(a) 9 lb·ft (c) 200 lb·ft
(b) 16 lb·ft (d) 400 lb·ft

10.17. A 5.0-N force acts tangentially on the rim of a wheel of radius 36 cm. Starting from rest, the wheel makes 10 rev in
4.0 s. The moment of inertia of the wheel is
(a) 0.11 kg·m 2 (c) 0.46 kg·m 2
(b) 0.23 kg·m 2 (d) 1.44 kg·m 2
10.18. An engine turning at 3000 rev/min develops 75 kW. The torque on the engine’s shaft
(a) is 2.6 N·m (c) is 239 N·m
(b) is25N·m (d) depends on the shaft radius

Supplementary Problems

10.1. Two identical balls move down an inclined plane. Ball A slides down without friction and ball B rolls down. Do the
balls reach the bottom together? If not, which is first? Why?
10.2. An aluminum cylinder of radius R, a lead cylinder of radius R, and a lead cylinder of radius 2R all roll down the
same inclined plane. In what order will they reach the bottom?
10.3. A square and a rectangle of the same mass are cut from a sheet of metal. Which has the greater moment of inertia
about a perpendicular axis through its center?

10.4. (a) Express 12.5 rev in radians. (b) Express 0.2 rad in revolutions. (c) Express 3π rad in revolutions.