Potential Energy / linear and angular velocity

[wooram83]

1. A cylinder, of mass 2 kg, and a radius of 1 m, starts from rest, at point A, with its axis 3.5m above a flat stretch of ground, then rolls down a 30 degree slope as shown. After rolling a few meters horizontally, it rolls up another 30 degree slope and emerges on a flat surface 2 m above the
ground, still rolling.
Assuming no loss to friction, and the acceleration of gravity is 9.80 m/s2:
a) Find the kinetic and potential energy of the cylinder at point A
b) Find the kinetic and potential energy of the cylinder at point B
c) Find the kinetic and potential energy of the cylinder at point C
Be sure to define the origin of potential energy (where PE = 0)
d) Find the linear and angular velocity of the cylinder at point A
e) Find the linear and angular velocity of the cylinder at point B
f) Find the linear and angular velocity of the cylinder at point C

Homework Equations

I=1/2MR^2

The Attempt at a Solution

a) KE=0, PE=68.6J
b) PE=0, KE=68.6J
c) PE= 39.2J, KE=29.4J
d) both=0
e) w=6.8 rad/s, v=6.8 m/s
f) w=5.1 rad/s, v=5.1m/s

I wasn't sure where to base the height on this question for the potential energy. The book says I have to measure from the center of mass but when the ball is on the ground the center of mass is located 1m above the ground. Do I still consider this Potential Energy zero or do I need to put 1m as the height? If I consider this to be zero at the ground than do I measure the original Potential Energy at the bottom of the ball? Please check my other work as well.

 

[gneill]

I wasn't sure where to base the height on this question for the potential energy. The book says I have to measure from the center of mass but when the ball is on the ground the center of mass is located 1m above the ground. Do I still consider this Potential Energy zero or do I need to put 1m as the height? If I consider this to be zero at the ground than do I measure the original Potential Energy at the bottom of the ball?

You could make ground + 1m the zero reference. Or you could make the initial height of the center of mass the zero reference. Or you could put it 100m below ground. As long as you keep track of the signs as things shift around, everything will work out.

Some people find it easier to keep things straight by identifying the point of lowest potential in the problem and calling it the zero reference. That way, everything will always have positive (or zero) potential and there's no signs to muck up.

So sure, put your zero reference at the height of the center of mass of the cylinder at its lowest.