angular speed of the ball = 15.2 rev/s
diameter = 21.6 cm
radius = 10.8 cm
mass = 7.27 kg
Moment of inertia of ball is given as
[tex]I = \frac{2}{5}mR^2[/tex]
[tex]I = \frac{2}{5}\time 7.27\times (0.108)^2[/tex]
[tex]I = 0.034 kg m^2[/tex]
now angular acceleration is defined as rate of change in angular velocity
[tex]\alpha = \frac{\omega_f - \omega_i}{t}[/tex]
[tex]\alpha = \frac{2\pi (15.2) - 0}{0.525}[/tex]
[tex]\alpha = 182 rad/s[/tex]
now we know that
[tex]\tau = I \alpha[/tex]
[tex]\tau = 0.034 \times 182 = 6.18 Nm[/tex]
so it requires a torque of 6.18 Nm
