Question

Review Multiple-Concept Example 7 in this chapter as an aid in solving this problem. 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 0.602 m. At one point on this circle, the ball has an angular acceleration of 64.1 rad/s2 and an angular speed of 13.0 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.

Answer 1

108.8 m /s

θ = 21°

Step-by-step explanation:

Centripetal acceleration = ω² R

=( 13 )² x .602

= 101.74 m/s²

tangential acceleration a_t = angular acceleration x R

= 64.1 x .602

= 38.58 m /s²

Total acceleration R

R² = ( 101.74 )² + ( 38.58 )²

R = 108.8 m /s

angle required be θ

Tanθ = tangential accn / radial accn

= 38.58 / 101.74

θ = 21°