please solve this problem 3 Find the angular speed of an obj

please solve this problem

3. Find the angular speed of an object travelling around a circle in revolution/min, given that the linear speed of the object is 30 feet sec and the radius of the circle is 10 feet.

Solution

Formula connecting linear speed and angular speed:

v = r w

where v is the linear speed, r is the radius of the circle and w is the angular speed.

In the question, we are provided with the linear speed and radius

v = 30 feet/sec

r = 10 feet

v = rw

w = v/r

w = 30/10 = 3 rad/s

To convert radians per second to revolution per minute

we need to multiply

(3 rad / 1 sec) x (1 rev / 2 rad) x (60 sec / 1 min) = 28.647 rev /min

So angule speed is  28.647 rev /min .