Page 128 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 10] ROTATIONAL MOTION 113

Angular velocity is usually expressed in radians per second (rad/s), revolutions per second (rev/s or rps), and
revolutions per minute (rev/min or rpm), where

1 rev/s = 2π rad/s = 6.28 rad/s
2π
1 rev/min = rad/s = 0.105 rad/s
60
The linear velocity v of a particle that moves in a circle of radius r with the uniform angular velocity ω is
given by

v = ωr
Linear velocity = (angular velocity)(radius of circle)

This formula is valid only when ω is expressed in radian measure.

SOLVED PROBLEM 10.1

(a) Express 6 rev in radians. (b) How many revolutions are equivalent to 10 rad? (c) How many revolutions
are equivalent to π/2 rad?
2π rad

◦
(a) θ = (8 ) = 0.14 rad
360 ◦
360 ◦

(b) θ = (2.5 rad) = 143 rad
2π rad
360 ◦

(c) θ = π rad = 180 ◦
2π rad
SOLVED PROBLEM 10.2
(a) Express 8 in radians. (b) Express 2.5 rad in degrees. (c) Express π rad in degrees.
◦
◦
(a) θ = (8 )(0.01745 rad/ ) = 0.14 rad
◦
◦
(b) θ = (2.5 rad)(57.3 /rad) = 143 rad
◦
360
(c) θ = (π rad) = 180 ◦
2π rad
SOLVED PROBLEM 10.3
The shaft of a motor rotates at 1800 rev/min. Through how many radians does it turn in 18 s?

The angular velocity in radians per second that corresponds to 1800 rev/min is

2π rad/rev
ω = (1800 rev/min) = 189 rad/s
60 s/min
Since ω = θ/t, in 18 s the shaft turns through
θ = ωt = (189 rad/s)(18 s) = 3402 rad

SOLVED PROBLEM 10.4
◦
A phonograph record 30 cm in diameter turns through an angle of 200 . How far does a point on the rim
of the record travel?