A baseball pitcher,loosening up his arm before a game,tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 12 m/s in a time of 0.40 s,what is the average angular acceleration of the arm and ball? A)0.067 rad/s² B)94 rad/s² C)15 rad/s² D)37 rad/s²

Question

Quizplus · Accepted Answer

The average angular acceleration can be calculated using the formula α = Δω/Δt, where Δω is the change in angular velocity and Δt is the change in time. First, find the final angular velocity ω using v = rω, where v is the linear velocity and r is the radius (0.32 m). So, ω = v/r = 12 m/s / 0.32 m = 37.5 rad/s. Since the ball starts from rest, the initial angular velocity is 0 rad/s. Therefore, Δω = 37.5 rad/s - 0 rad/s = 37.5 rad/s. The time Δt is 0.40 s. Thus, the average angular acceleration α = 37.5 rad/s / 0.40 s = 93.75 rad/s², which rounds to 94 rad/s².

A Baseball Pitcher,loosening Up His Arm Before a Game,tosses a 0.15-Kg