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WAEC Physics 2014 Paper

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Question : 2

Total: 48

An object of mass m moves with a uniform speed v round a circular path of radius r. If its angular speed is

\omega

, the magnitude of the centripetal force acting on it is

$m \omega^2 r$
$\; \frac{m v^2}{r}$
$m \omega r$
$\; \frac{m v^2}{r^2}$

Solution:

Concept:

For uniform circular motion, centripetal force can be written in terms of angular speed as

F = m \omega^2 r

.

Explanation:

The general expression for centripetal force is

F = \dfrac{mv^2}{r}

.

The linear speed

v

is related to angular speed

\omega

by

v = \omega r

.

Substitute

v = \omega r

into the force equation:

F = \frac{m(\omega r)^2}{r} = m\omega^2 r

Thus, the magnitude of the centripetal force acting on the object is

m\omega^2 r

.

Answer:

Option A:

m\omega^2 r

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