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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 tex2html_wrap_inline916 and the kinetic energy is zero. So the total energy is tex2html_wrap_inline918 .

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. tex2html_wrap_inline920 . Therefore


To get the acceleration a, note that tex2html_wrap_inline924 . 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 tex2html_wrap_inline926 , so tex2html_wrap_inline928 .

If it's solid then tex2html_wrap_inline930 , so tex2html_wrap_inline932 .

It accelerates faster if the cylinder is solid.

Joshua Deutsch
Sun Feb 23 15:54:50 PST 1997