A ball with mass m=15g at the end of a massless string is swinging in a circle o

Question

A ball with mass m=15g at the end of a massless string is swinging in a circle of redius R= 1.3m with and angular velocity w=4 rad/s.

Part A. Write an expression for the velocity v of the ball.

Part B. Calculate the velocity of the ball, v in m/s.

Part C. In order to travel in a circle, the direction the balls path ust constantly be changing (curving inward). This constant change in direction towards the center of the circle is center pointing acceleration called centripetal acceleration ac. Write an expression for the centripetal acceleration ac of the ball, in terms of the linear velocity.

Part D. Calculate the centripetal acceleration of the ball, ac in m/s^2.

Explanation / Answer

A)The velocity of the ball will be:

v = r w

B) v = 1.3 x 4 = 5.2 m/s

Hence, v = 5.2 m/s

C)The centripital acceleration is:

a(c) = v^2/R

D)a(c) = v^2/R = 5.2^2/1.3 = 20.8 m/s^2

Hence, a(c) = 20.8 m/s^2

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