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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 24 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?Select one:a.94 rad/s2b.0.067 rad/s2c.15 rad/s2d.190 rad/s2

Question

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 24 m/s in a time of 0.40 s, what is the average angular acceleration of the arm and ball?Select one:a.94 rad/s2b.0.067 rad/s2c.15 rad/s2d.190 rad/s2

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Solution

To solve this problem, we first need to find the linear acceleration of the ball. This can be found using the formula:

a = Δv / Δt

where Δv is the change in velocity and Δt is the change in time.

Given that the ball starts at rest and is released with a speed of 24 m/s in a time of 0.40 s, we can substitute these values into the formula:

a = (24 m/s - 0 m/s) / 0.40 s = 60 m/s²

Next, we need to find the angular acceleration. Angular acceleration (α) can be found using the formula:

α = a / r

where a is the linear acceleration and r is the radius (or in this case, the length of the forearm).

Substituting the given values into the formula:

α = 60 m/s² / 0.32 m = 187.5 rad/s²

However, this value is not in the options. There might be a mistake in the problem or the options. The closest option to the calculated value is:

d. 190 rad/s²

This problem has been solved

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