What is uniform circular motion:? The blades of an aeroplane propeller are rotating at the rate of 600 revolutions per minute: Calculate its angular velocity.

Explanation

A particle is said to be in uniform circular motion, if it moves along the path of a circlesuch that .. . time rate of change of angular position of particle is constant.
Relationship between angular velocity and angular acceleration
We know `omega = ( d theta)/( dt ) " "...(i) `
Defferentiating equation (i) w.r.t. time .t. , we have
`(d omega )/( dt ) = alpha = ( d)/(dt) ((d theta)/( dt ))`
`implies a = (d ^(2) theta)/( dt ^(2)) = (d omega )/( dt ) " "...(ii)`
Equation (ii) gives relationship between angular velocity and acceleration.
We know that
Angular velocity `(omega) = 2 pi u.`
Here, `u = 600 rpm = ( 600)/( 60) = 10 ` r.p. s.
Therefore `omega = 2 pi u = 2 pi xx 10 implies omega = 20 pi rad s ^(-1).`