In a fast-pitch softball game the pitcher is impressive to watch, as she deliver

Question

In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. In one instance, the radius of the circle is 0.621 m. At one point on this circle, the ball has an angular acceleration of 63.9 rad/s2 and an angular speed of 12.3 rad/s. (a) Find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) Determine the angle of the total acceleration relative to the radial direction.

Explanation / Answer

r=0.621 m
=63.9 rad/s2
= 12.3 rad/s
the centripetal and tangential accelerations are
ac = ²r=12.3^2*0.621=93.95 m/s^2
and
at = r=39.68m/s^2
since the accelerations are at right angles,
the magnitude of the total acceleration
a = [ac² + at²] = [(²r)² + (r)²] = 102m/s²
and its direction is
= arctan(ac/at) = arctan(²/) = 67.1degree from the direction of motion on the inside of the curve

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