Page 140 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 10] ROTATIONAL MOTION 125

10.5. (a) Express 32 in radians. (b) Express 4.8 rad in degrees. (c) Express π/8 rad in degrees.
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10.6. The minute hand of a clock is 40 cm long. How many centimeters does its tip move in 25 min?
10.7. A drill bit 1 in. in diameter is turning at 400 rev/min. (a) What is its angular velocity in radians per second? (b) What
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is the linear velocity in feet per second of a point on its circumference?

10.8. The teeth of a certain circular saw blade are supposed to move at 15 m/s. If the blade is 60 cm in radius, at how many
revolutions per minute should it turn?

10.9. A car whose tires have radii of 50 cm travels at 20 km/h. What is the angular velocity of the tires?
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10.10. The earth’s radius is 6.4 × 10 m. (a) Through how many radians does the earth turn in 1 year? (b) How far does a
point on the equator move in 1 year owing to this rotation?
10.11. A grindstone that is rotating at 2000 rev/min requires 50 s to come to a stop when its motor is switched off. (a) Find
the angular acceleration of the grindstone. (b) How many radians does it turn through before stopping? (c) Through
how many revolutions?

10.12. A wheel rotating at 20 rev/s is brought to rest by a constant torque in 12 s. How many revolutions does it make in
this time?

10.13. The propeller of a ship makes 300 rev while its speed increases from 200 to 500 rev/min. (a) What is its angular
acceleration? (b) How much time did the increase in speed require?

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10.14. The mass and radius of the earth are, respectively, 6 × 10 24 kg and 6.4 × 10 m. Assuming that it is a sphere of
uniform density (which is not the case, since the earth’s metallic core has a greater density than the mantle of rock
around it), find the moment of inertia of the earth.

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10.15. The moment of inertia of a 45-kg grindstone is 5 kg·m . Find its radius of gyration.
10.16. A solid cylinder and a hollow cylinder of the same mass and diameter, both initially at rest, roll down the same
inclined plane without slipping. (a) Which reaches the bottom first? (b) How do their kinetic energies at the bottom
compare?

10.17. A bowling ball rolling at 8 m/s begins to move up an inclined plane. What height does it reach?

10.18. A certain engine develops 40 hp at 1000 rev/min and 65 hp at 1600 rev/min. At which angular velocity does it
produce the greatest torque?

10.19. The alternator on a truck engine produces 350 W of electric power when it rotates at 4000 rev/min. If it is 95 percent
efficient, what should the difference (in newtons) between the tensions in the tight and slack parts of its V-belt drive
be? The diameter of the alternator’s pulley is 10 cm.
10.20. The anchor windlass of a boat is required to pull a load of 400 lb at 2 ft/s. (a) How many horsepower are required?
(b) If the windlass drum is 8 in. in diameter, at how many revolutions per minute should it turn? (c) What torque is
developed by the drum?

10.21. A constant frictional torque of 200 N·m is applied to a turbine initially rotating at 120 rad/s, and it comes to a stop
in 80 s. What is the turbine’s moment of inertia?

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10.22. A rotating cylindrical flywheel of mass 1 × 10 kg and radius 2 m has been proposed for energy storage. (a) What
is its KE when it rotates at 400 rad/s? (b) For how many hours can it supply energy at the rate of 1 MW?
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10.23. A wheel whose moment of inertia is 2 kg·m has an initial angular velocity of 50 rad/s. (a) If a constant torque of
10 N·m acts on the wheel, how long does it take to be accelerated to 80 rad/s? (b) By how much does its kinetic
energy increase?