It is a vector quantity with an SI unit of metres per second (m s1). It has the same meaning in circular motion as it does in linear motion.
Relationship between Angular Velocity
and Linear Velocity The derivations of the relationship between angular and linear velocity is required. Equation:
v r
DERIVATION OF FORMULA v r Derivation: Based on the definition of linear speed we have
aspeed distance travelled time taken
b Based on the definition of angle a s Combining these two equations we get V
r b v s
t we get r s
v r t
By combining that equation with the definition of angular velocity
v r t Qv
t r Q v vr
RELATIONSHIP BETWEEN ANGULAR VELOCITY AND LINEAR VELOCITY
v r v linear velocity
angular velocity r radius
av t b
we get:
SAMPLE PROBLEM 6A
A motorcyclist performing the ‘circle of death’ travels at constant speed in a circular path. (i) What is the angular velocity if he completes 12 revolutions in 10 s? (ii) What is his speed if the radius of the circle of death is 5 m?
SAMPLE ANSWER 6A (i) Using the formula for angular velocity, making sure all values are in their standard unit:
v t 12 : 2p
10 2.4p
The cyclist’s angular velocity is 2.4rad s1, which is equal to 7.536 rad s1. (ii) v r (7.536)(5) 37.68 The cyclist has a speed of 37.68 m s1.
