Page 133 - Schaum's Outline of Theory and Problems of Applied Physics

118 ROTATIONAL MOTION [CHAP. 10

SOLVED PROBLEM 10.11
The starting cord of an outboard motor is wound around a pulley 18 cm in diameter that is attached to the
motor’s crankshaft. How much torque is applied to the crankshaft when the cord is pulled with a force of
50 N?

Here the moment arm of the force is the pulley’s radius of 9 cm = 0.09 m. The torque is therefore
τ = Fr = (50 N)(0.09 m) = 4.5N·m

SOLVED PROBLEM 10.12
2
A flywheel whose moment of inertia is 6 kg·m is acted upon by a constant torque of 50 N·m. (a) What
is its angular acceleration? (b) How long does it take to go from rest to a velocity of 90 rad/s?
τ 50 N·m
(a) α = = = 8.33 rad/s 2
I 6kg·m 2
90 rad/s
ω f − ω 0
(b) t = = = 10.8s
α 8.33 rad/s 2
SOLVED PROBLEM 10.13

The winding drum of an elevator is 4 ft in diameter. (a) At how many revolutions per minute should the
drum rotate in order to raise the cab at 500 ft/min? (b) If the total load is 2 tons, how much torque is
required?
(a) Since
500 ft/min
v = = 8.33 ft/s
60 s/min
the angular velocity of the drum must be
v 8.33 ft/s
ω = = = 4.17 rad/s
r 2ft
which is

60 s/min
ω = (4.17 rad/s) = 39.8 rev/min
2π rad/rev
(b) Since 1 ton = 2000 lb, the required torque is
τ = Fr = (4000 lb)(2ft) = 8000 lb·ft

ROTATIONAL ENERGY AND WORK
The kinetic energy of a body of moment of inertia I whose angular velocity is ω (in rad/s) is

1
KE = Iω 2
2
1
Kinetic energy = ( )(moment of inertia)(angular velocity) 2
2
The work done by a constant torque τ that acts on a body while it experiences the angular displacement θ
rad is
W = τθ

Work = (torque)(angular displacement)