During your tennis serve, your racket and arm move in an approximately rigid are

Question

During your tennis serve, your racket and arm move in an approximately rigid are with the top of the racket 1.5 m from your shoulder joint. The top accelerates from rest to a speed of 20 m/s in a time interval of 0.10 s. Determine the magnitude of the average tangential acceleration of the top of the racket. Express your answer to two significant figures and include the appropriate units. Find the magnitude of the rotational acceleration of your arm and racket. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given : - tangential velocity = 20m/s

time interval during which it accelerates =0.1 s

radius = 1.5 m

using the equation of motion we have

v = u + at

20 = 0 + a *(0.1)

a = 20/0.1 = 200m/s

so the tangential acceleration is 200m/s2

b) tangential acceleration =rotational acceleration * radius

a = r*alpha

alpha =a/r = 200/1.5 = 133.33 rad/s2

so the rotational acceleration of the arm is 133.33 rad/s2

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