Question

A car is going at a uniform speed of 25.0 miles per hour on a circular...

A car is going at a uniform speed of 25.0 miles per hour on a circular horizontal road of radius 50.0 meters. (a) Find the magnitude and the direction of its centripetal acceleration when it is at the southernmost point on the road. (b) What is its angular velocity?

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Homework Answers

Answer #1

Given

Speed v = 25 miles/ hour

v = 11.176metre/second (1miles/hour = 0.447metre/second)

Radius r = 50 m

Centripetal acceleration a​​​​​​ c = v​​​​​​ 2 / r = 2 r

= angular velocity

a c = v 2 / r

a c = ( 11.176) 2 / 50

a c = 2.5 m / s 2

The magnitude of the centripetal acceleration = 2.5 m/ s​​​​​​ 2 . The direction is towards the centre of the circle . ie, directed towards left .

b .

a c = 2 r

=√( a c / r )

= √ ( 2.5 / 50 )

= 0. 2236 s -1

The angular velocity = 0.2236 s -1

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