Question

A small block with mass 0.350 kg is attached to a string passing through a hole in a frictionless, horizontal surface. The block is originally revolving in a circle with a radius of 0.500 m about the hole with a tangential speed of 1.50 m/s, uniformly. Consider the block as a particle. Moment of inertia of a particle is I=mr2, where r is the radius of the circle. Of course a tension force of the string is holding the block on the orbit. The string is then pulled slowly from below, shortening the radius of the circle to 0.250 m. What is the initial angular velocity of the block? Calculate the centripetal acceleration of the block and the magnitude of tension force holding the block in the orbit of radius 0.5 m. Is the angular momentum conserved? Why? (n) (y) Explain. What is the new angular velocity? What is the new tangential velocity What is the new centripetal acceleration?

Answer 1

Angular velocity

Initially

v = 1.50 m/s

r = 0.500m

Initial angular velocity

Centripetal acceleration

Centripetal force will be provided by the tension in the string. So,

Tension in string = Centripetal Force

Yes, Angular momentum is conserved because there is no torque acting.

According to Law of conservation of angular momentum

Where moment of inertia is

So

New angular velocity is 12 rad/sec

New tangential velocity

New Centripetal acceleration