Angular Speed Formula

What is Angular Speed?

Angular speed is the rate at which an object rotates around a central point or axis. That is, it tells one how fast an object turns through an angle. It is measured in radians per second (rad/s) or degrees per second (°/s).

Definition: Angular speed refers to how much angle, in radians or degrees, that an object rotates in any given amount of time.

Formula 

Angular Speed Formula calculates distance travelled in terms of number of revolutions or rotations to the time taken. It is measured in ω and given by,

Units of distance traveled = ω units of time taken

The Distance travelled is denoted as θ and expressed in radians. The time consumed is measured in terms of seconds. Therefore, the angular speed is stated in radian per seconds or rad/s.

Angular speed for a single complete rotation is referred to as

 

The relationship of Angular speed and Linear Speed is,

 

Where,

• v = Linear speed

• R=The radius of the circular path

Solved Problems

Problem 1: Earth takes 365 days to complete a revolution around the sun. Calculate its angular speed.

Solution:

The formula of angular speed is given as,

 

Where

t = 365 24 60 60

  = 31536000 s

       

       = 1.9923 10-7 rad/s.

Problem 2: The wheel of a wagon of radius 1m is travels at the speed of 5m per second. Calculate its angular speed.

Solution:

Given,

Linear speed V = 5m/s,

Radius of circular path r = 1m

Substituting the values, we obtain

5 /1= 5 rad/s

Conclusion

Understanding angular speed is essential for analyzing motion in rotational systems. You can grasp the concept effectively by practicing with the formula and applying it to various scenarios. 

 

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