Question

a point on the rim of a wheel moves with a velocity of 80 feet per second. What is the angular velocity of the point if the diameter of the wheel is 10 feet

Answer 1

The angular velocity is 16 radians per second

Solution:

The angular velocity of point is given by formula:

$w = \frac{v}{r}$

Where,

w is the angular velocity in radians

v is the linear velocity

r is the radius

Given that diameter of wheel is 10 feet

$radius=\frac{diameter}{2}$

$radius = \frac{10}{2}=5$

Thus radius is 5 feet

A point on the rim of a wheel moves with a velocity of 80 feet per second

Linear velocity = v = 80 feet per second

Therefore, angular velocity is given as:

$w = \frac{80}{5} = 16$

Thus angular velocity is 16 radians per second