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A wheel with diameter 35 cm is rotating at 20 revolutions per minute. what is the speed of the rotating wheel in radians per second. This is the angular velocity of the wheel.

Sagot :

Since we are just being asked about giving the angular velocity (ω) of the rotating wheel in rad/s, we do not need to take into account the diameter of the wheel.

We only do that when the linear velocity is being asked. v=rω

Anyway.

So we are given with [tex]20 \frac{rev}{min} [/tex] and we want to make the unit as [tex] \frac{rad}{s} [/tex].

In order to do that, we just have to remember that 1 revolution=2π rad

Doing the necessary conversions:
[tex]20 \frac{rev}{min} * \frac{1 min}{60 s}* \frac{2 \pi rad}{1 rev} [/tex]

By doing the arithmetic you will be able to get the value of the angular velocity in rad/s.

Hope that helps.