Question

A wheel rotates with a constant angular velocity of 300 r.p.m. The angle through which the wheel rotates in one second i

Answer 1

Angular Velocity = 300 r.p.m.

1 revolution = 2π radians

So without using revolutions per minute, we can rewrite the Angular velocity by using angle in radians.

Angular Velocity = 300 x 2π radians per minutes

                           = 600π radians per minutes

So, if  this wheel rotates 600π per minute,

Angle which the wheel rotates per second = 600π/3600

                                                                       = π/6 radians

Answer 2

Given:

Angular Velocity = 300 r.p.m

To find:

The angle through which the wheel rotates in one second.

Solution:

According to the law of angular velocity and momentum,

One revolution is twice the angle of rotation.

That is,

1 revolution = 2π radians

Representing angular velocity in radians,

Angular Velocity = r.p.m * 2π radians per minute

Angular Velocity = 300 * 2π radians per minute

Therefore,

Angle which the wheel rotates per minute = 600π radians

Converting minute to second,

Divide by 3600,

Angle which the wheel rotates per second = Angle which the wheel rotates per minute / 3600

The angle through which the wheel rotates per second =  π/6 radians