A bicycle wheel can be thought of simply as a centralsolid cylinder (the part that attaches to the axle) surrounded by athin shell of mass (the rim and tire) located along the outer edgeof the wheel. Compared to these parts of the wheel, the mass of thespokes is small enough to be neglected. A sample bicycle wheel hasmass 2.0 kg, half of which is in the central cylinder. The otherhalf is in the rim and tire. The central cylinder has a radius of4.0 cm (note the unit!). The wheel has a radius of 40.0cm.

a) What is the moment of inertia of the central cylinder?

b) What is the moment of inertia of the rim/tire? Hint: youshould not be using the same equation you used in (a).

c) The moment of inertia of the entire wheel is just the sum ofthe individual moments of inertia of the parts. What is the momentof inertia of the wheel?

The wheel described above rolls down a ramp withoutslipping. It starts rolling on the ramp at a point where the rampis 2.0 m above the ground. Any energy lost to frictional effects asthe wheel rolls is negligible.

d) What gravitational potential energy (relative to the ground)does the wheel have at the top of the ramp?

e) What types (plural!) of mechanical energy does the wheel havewhen it reaches the ground?

f) How fast is the wheel moving at the bottom of the ramp? Hint:This is asking for the translational velocity of the wheel. Youneed to set up an energy conservation equation in which you canisolate the translational velocity as the only unknownquantity.

g) Assuming acceleration is constant, what is the averagetranslational velocity of the wheel as it rolls down the ramp?Hint: since the wheel started from rest, the relationship betweenthe average velocity and the velocity at the bottom of the ramp isquite simple; go back to your kinematics equations!