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 = `\frac {d}{2}` = `\frac {1.5 m}{2}` = 0.75 m

To Find:
Angular speed = Ѡ = ? 

Solution:

The formula for Angular speed Ѡ  is 

Ѡ = `\frac {v}{r}`

by putting values 

Ѡ = `\frac {30 m s⁻¹}{0.75 m}`

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 = `\frac {1}{2π}` rev

thus, 

Ѡ = 40 rad s⁻¹ = `\frac {40}{2π}` rev s⁻¹= `\frac {20}{π}` rev s⁻¹ = 6.36 rev s⁻¹ ----------------Ans.



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