Examples

Examples of Questions Solved with the Help of Angular Velocity (or speed) Formula

Example 1:- Earth takes a whole year (365 days) to complete a single revolution around the sun. Calculate the angular speed with which the earth is rotating around the sun.

Solution: The plane earth requires a full year to make a single rotation around the sun. So, the time taken in second will be 

t = 265 × 24 hr × 60 min/hr × 60 sec/min = 31,53,60,00 seconds.

The earth completes make a single full rotation, and one rotations covers 360^o, so the can be written as = 2π.

And after substituting these values in the formula of angular speed,

Angular speed (ω)    =

TotalDistanceCoveredTotalTimeTaken����������������������������������

=

ΘtΘ�

        =

2π31,53,60,00sec2�31,53,60,00���

= 1.9923 × 10^-7 rad/sec.

Thus the angular velocity of earth while moving around the circle will be 1.9923 × 10^-7 rad/sec.

Example 2:- The wheels of a huge truck of radius 1m is travelling with the speed of 5m per second. Calculate its angular speed.

Solution: The travelling speed of the truck can be considered as the Linear speed is = 5m/s,

The radius of the wheel of a truck (or the circular path) id r = 1 m (given)

The formula used to find the angular velocity ω = r   

Substituting the values, we get

 ω =

5151

= 5 rad/sec.

Hence the angular speed of the wheels of that truck will be equal to 5 rad/sec.

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