derive a relation between angular speed ( w ) and RPM ( N )
Answers
Explanation:
Both the quantities are used in physics where there is a rotation.
Angular velocity is the rate of change of angle with respect to time. Unit of angular velocity is radians per second (rad/sec).
It's a vector quantity who's direction is given by the right hand thumb rule
dθdt=ω=2πN60
θ is the angle turned in radians
ω is the angular velocity in radians per second ( rad/s)
N is the Revolution per Minute ( RPM ).
Both the quantities are used to express the rotational speed. RPM is used when the rotational speed is very low. (so converting into time for a minute, it would give a recognizable quantity). But rad/s is used for reasonably high speed rotation.
1 RPM means, in 1 minute the object completes one revolution and 1 rad/s means in 1 second the object completes in radian. one complete revolution is equals to 2π radians. ( 6.28.. approximately).
Unit of ω is radians per second (rad/s), dimension of ω is [s−1]
Unit of N is revolutions per minute often called rpm. Dimension of N is also [s−1]