To solve this problem we will apply the concepts given about acceleration in rectilinear motion and angular movement. Tangential acceleration can be described as the change of the final and initial velocity in an instant of time, that is,
[tex]a = \frac{v_f-v_i}{t}[/tex]
Our velocities are given as,
[tex]v_i = 0[/tex]
[tex]v_f = 12m/s[/tex]
And the time taken to increase the speed of the ball is t = 40s
[tex]a = \frac{12-0}{0.4s}[/tex]
[tex]a = 30m/s^2[/tex]
The length of the forearm is [tex]r = 0.32m[/tex]
The angular acceleration is defined as the change of the tangential acceleration in proportion to the turning radius, therefore
[tex]\alpha = \frac{a}{r}[/tex]
[tex]\alpha = \frac{30}{0.32}[/tex]
[tex]\alpha = 93.75rad/s^2[/tex]
Therefore the angular acceleration of the arm and ball is [tex]\alpha = 93.75rad/s^2[/tex]
