Question

A hoop and a solid cylinder have the same mass and radius. They both roll, without slipping, on a horizontal surface. If their kinetic energies are equal

• A. The hoop has a greater translational speed than the cylinder
• B. The cylinder has a greater translational speed than the hoop
• C. The hoop and the cylinder have the same translational speed
• D. the hoop have greater rotational speed than the cylinder.

Answer 1

The correct option is B The cylinder has a greater translational speed than the hoop

Kinetic energy is equal

$I_1{\omega }_1^2=I_2{\omega }_2^2$

$\frac{{\omega }_1}{{\omega }_2}=\sqrt{\frac{I_2}{I_1}}$

Inertia of hoop will be larger because $I_2=m{r}^2$

Inertia of cylinder is $I_1=\frac{1}{2}m{r}^2$

Since $I_2>I_1,{\omega }_1>{\omega }_2$

translation speed $v_1={\omega }_{1}r$

So cylinder has a greater translational speed than the hoop.