Answer
The thin-walled spherical shell has greater moment of inertia. Its deceleration is smaller and therefore, it takes a longer time for that shell to come to a halt.
The time it takes for the solid sphere to stop: $t_1=4.8s$
The time it takes for the thin-walled sphere to stop: $t_1=8s$
Work Step by Step
i) From Table 9.1, a solid sphere with axis through center has $I=2/5MR^2$, while a thin-walled sphere with axis through the center has $I=2/3MR^2$.
Therefore, the thin-walled spherical shell has greater moment of inertia.
ii) The torque produced by friction will cause the sphere to decelerate, following the equation: $$\tau=I\alpha$$
Because the thin-walled shell has greater $I$, the magnitude of its deceleration will be smaller.
iii) Because the magnitude of the thin-walled shell's deceleration is smaller, it will take a longer time for the thin-walled shell to come to a halt.
The deceleration of each sphere is:
- Solid sphere: $$\alpha_1=\frac{-\tau}{\frac{2}{5}MR^2}=\frac{-0.12N.m}{\frac{2}{5}(1.5kg)(0.2m)^2}=-5rad/s^2$$
- Thin-walled sphere: $$\alpha_2=\frac{-\tau}{\frac{2}{3}MR^2}=\frac{-0.12N.m}{\frac{2}{3}(1.5kg)(0.2m)^2}=-3rad/s^2$$
The time it takes for each sphere to stop is
- Solid sphere: $$t=\frac{\omega-\omega_0}{\alpha_1}=\frac{0-24rad/s}{-5rad/s^2}=4.8s$$
- Thin-walled sphere: $$t=\frac{\omega-\omega_0}{\alpha_2}=\frac{0-24rad/s}{-3rad/s^2}=8s$$
