Question

A cylinder of mass 30 kg and radius 2 meters is rolling on a table without sliding. If its velocity is 4 meters per second then calculate its kinetic energy.​

Answer 1

The kinetic energy of a rolling object is calculated like so:

KE=12mv2+12Iω2KE=12mv2+12Iω2

where mm is the mass, vv is the velocity, II is the moment of inertia of the object, and ωω is its angular velocity.

The first term is easy: we know the mass and velocity, so we just plug them in. To calculate the second term we would seem to need to know the radius of the cylinder. I mean, for a cylinder:

I=12mr2I=12mr2

and we can calculate the angular velocity from v and r:

ω=vrω=vr

Puzzling, but that makes the second term:

12Iω2=1212mr2(vr)212Iω2=1212mr2(vr)2

=14mr2v2r2=14mr2v2r2

and the r-squared terms cancel out, leaving

= 14mv214mv2

So the total answer is:

KE = 12mv2+14mv2=34