Page 13 - 11-phy-5 Circular Motion

5. Circular Motion eLearn.Punjab
It can, therefore, be concluded that:

The instantaneous acceleration of an object travelling with uniform speed in a circle is directed
towards the centre of the circle and is called centripetal acceleration.

The centripetal force has the same direction as the centripetal acceleration and its value is given by

mv 2 Tid-bits
r
=Fc m=ac ............ (5.14)

In angular measure, this equation becomes

F=c mrw2 ........... (5.15)

Example 5.2: A 1000 kg car is turning round a corner at 10 ms-1

as it travels along an arc of a circle.If the radius of the circular path
is 10 m, how large a force must be exerted by the pavement on the
tyres to hold the car in the circular path?

Solution : The force required is the centripetal force. Curved flight at high speed requires
a large centripetal force that makes
So the stunt dangerous even if the air
planes are not so close.

=Fc m=v 2 1000 kg x 100 m=2s-2 1.0 x 104kgms-2 = 1.0 x 104N
r 10 m

This force must be supplied by the frictional force of the

pavement on the wheels.

Example 5.3: A ball tied to the end of a string, is swung in a
vertical circle of radius r under the action of gravity as shown in
Fig. 5.7. What will be the tension in the string when the ball is at
the point A of the path and its speed is v at this point?

Solution: For the ball to travel in a circle, the force acting on the

ball must provide the required centripetal force. In this case, at

point A, two forces act on the ball, the pull of the string and the Fig. 5.7

weight w of the ball. These forces act along the radius at A, and so

their vector sum must furnish the required centripetal force. We, therefore, have

13 v: 1.1