We will use conservation of energy to solve the problem. You can also solve it using torques and forces.

Iniitally the potential energy, measured from *y* as shown is
and the kinetic energy is zero. So the total energy
is .

Finally, the potential energy is zero, and from eqn. 1.34 we have the kinetic energy. Therefore

Therefore the answer to (a) is

To relate this to the distance travelled along the incline. . Therefore

To get the acceleration *a*, note that . Comparing with the above,
we have that answer to (b):

Now let's look at what happens for different kinds of cylinders. If the cylinder is hollow, then , so .

If it's solid then , so .

It accelerates faster if the cylinder is solid.

Sun Feb 23 15:54:50 PST 1997