Question

How to find rpm given speed and diameter?

Answer 1

Answer:

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Answer 2

Given:

Speed and diameter values are provided.

To find:

Angular velocity in terms of rpm ?

Calculation:

• Let speed (i.e. linear velocity magnitude) be 'v' m/s and diameter be 'd' metres .

So, the angular velocity in radians/sec :

$\rm \omega = \dfrac{v}{radius}$

$\rm \implies\omega = \dfrac{v}{ (\frac{d}{2}) }$

$\rm \implies\omega = \dfrac{2v}{ d} \: rad/sec$

Now, lets convert the unit to rpm :

• 1 second = 1/60 minute
• 1 radian = 1/2π revolutions

$\rm \implies\omega = \dfrac{2v}{ d} \times \dfrac{60}{2\pi}$

$\boxed{ \rm \implies\omega = \dfrac{60v}{\pi d} \: rpm}$

This is how we can calculate angular velocity in terms of rpm.