Question

A spherical shell of radius 3.84 cm and a cylinder of radius 7.22 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the spherical shell's angular speed to the cylinder's angular speed be?

Answer 1

R_shell = 3.84 cm

= 0.0384 m

R_cylinder = 7.22 cm

= 0.0722 m

first the moment of inertia of the shell is = 2/3 M R²

and speed is ₁ = v₁ / r₁

total KE_shell = 1/2 m v² + 1/2 I²

= 5/6 mv²

sameway

total KE_cylinder = 3/4 mv²

now if KE_shell and KE_cylinder are same then

V_shell / V_cylinder = ( 9/10 )^1/2

so

_shell R_shell /_cylinder R_cylinder = ( 9/10 )^1/2

_shell / _cylinder= ( 9/10 )^1/2 ( R_cylinder / R_shell )

= ( 9/10 )^1/2 ( 0.0722/ 0.0384 )

_shell / _cylinder= 1.7837222