Question

Review the multiple-concept example 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 on a circle. In one instance, the radius of the circle is 0.685 m. At one point on this circle, the ball has an angular acceleration of 63.8 rad/s2 and an angular speed of 15.0 rad/s. (a) Find the magnitude of the total acceleration (centripetal plus tangential) of the ball.

Answer 1

Total acceleration will be
`160.20rad/sec^2`

Step-by-step explanation:

We have given radius of the circle r = 0.685 m

Angular acceleration
`\alpha =63.8rad/sec^2`

Angular speed
`\omega =15rad/sec`

Centripetal acceleration will be

`a_c=\omega ^2r=15^2* 0.685=154.125rad/sec^2`

Tangential acceleration will be

`a_t=r\alpha =0.685* 63.8=43.7rad/sec^2`

(a) Total acceleration will be equal to

`a=√(a_t^2+a_c^2)`

`a=√(43.7^2+154.125^2)=160.20rad/sec^2`

So total acceleration will be
`160.20rad/sec^2`