Question

A hoop of mass and radius and a solid cylinder of mass and radius are rolling along level ground with the same translational speed. Which object has the greater total kinetic energy?

Answer 1

the kinetic energy of hoop will be more than kinetic energy of solid cylinder

Step-by-step explanation:

kinetic energy of rolling is given as

`KE = (1)/(2)mv^2 + (1)/(2)I\omega^2`

here we know that for pure rolling we have

`v = R \omega`

now we also know that

`I = mk^2`

here k = radius of gyration

now we have

`KE = (1)/(2)mv^2( 1 + (k^2)/(R^2))`

now we know that for

hoop

`(k^2)/(R^2) = 1`

for Solid cylinder

`(k^2)/(R^2) = (1)/(2)`

now the kinetic energy of hoop will be more than kinetic energy of solid cylinder