When a softball player swings a bat, she accelerates it from rest to an angular

Question

When a softball player swings a bat, she accelerates it from rest to an angular velocity of 12 radians per second in a time of 0.42 seconds, when it collides with the ball. What was the angular acceleration of the bat? Through what angle did the bat rotate during this time interval? What was the torque the player applied to the bat? Model the bat as a uniform rod with mass 1.2 kg and length 0.85 m. [l_rod = (1/3)ML^2] Calculate the linear velocity of bat at the point of contact with the ball, 0.5 m from the axis of rotation.

Explanation / Answer

a)

Since it starts from rest initial angular velocity was zero i.e Wo=0 ,So from

W=Wo+alpha*t

12 =0+alpha*0.42

alpha =28.57 rad/sec2

b)

angular displacement

theta =Wt =12*0.42

theta =5.04 rad

if answer was needed in degrees

theta =5.04*180/pi =288.77o

c)

Moment of inertia

I=(1/3)ML2 =(1/3)*1.2*0.852 =0.289 Kg-m2

Torque

T=I*alpha =0.289*28.57

T=8.26 N-m

d)

Linear velocity

V=RW =0.5*12

V=6 m/s

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