Question

A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s. (A) through what angle, in radians, does the wheel rotate in 1.0 s? (B) what is the linear speed of a point on the wheel's rim? (C) what is the wheel's frequency of rotation?

Answer 1

You said 2 revolutions every 0.08 seconds

1 revolution = 2pi radians.

A). The 'unit rate' is (2 rev) x (2pi / 0.08 sec) = 50pi radians/sec. =

157.1 radians per sec (rounded)

B). Radius of the wheel = 30 cm
Circumference = 2pi R = 60pi cm = 188.5 cm (rounded)

Rotation speed = 2 revs per 0.08 sec
Linear speed = 2 x 60pi cm per 0.08 sec

(120pi cm) / (0.08 sec) = 47.12 meters per sec

C). Frequency = (revs) per second

= (2) / (0.08 sec) = 25 per second .