A motor car is traveling at a speed of 30 m s⁻¹. If its wheel has a diameter of 1.5 m, find its angular speed in rad s⁻¹ and rev s⁻¹. (40 rad s⁻¹ 6.36 rev s⁻¹ )


Given:

Linear speed of the car = v = 30 m s⁻¹
Diameter of wheel = d = 1.5 m  So
Radius of Cylinder = r = d2 = 1.5m2 = 0.75 m

To Find:
Angular speed = Ѡ = ? 

Solution:

The formula for Angular speed Ѡ  is 

Ѡ = vr

by putting values 

Ѡ = 30ms⁻¹0.75m

Ѡ = 40 rad s⁻¹ ----------- Ans. 1 (in rad s⁻¹) 


To convert rad s⁻¹ to rev s⁻¹, we know that

1 rev = 2 𝝿 rad

or

1 rad = 12π rev

thus, 

Ѡ = 40 rad s⁻¹ = 402π rev s⁻¹= 20π rev s⁻¹ = 6.36 rev s⁻¹ ----------------Ans.



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