I know that if a ramp is steeper, larger theta, then the object rolling down will become faster. However, if the object is rolling up the ramp will it slow down like I think it should?

Question

How can I prove this?

When I try to prove it via a kinetmatics equation I keep getting that the final velocity would be greater for a larger theta.

Please help.

Answer 1

look at the kinetic energy

for rolling up
... the steeper the ramp, the faster the KE becomes gravitational PE

same holds true for rolling down, except the energy goes in the other direction