A bicycle wheel can be thought of simply as a central solid cylinder (the part that...

A bicycle wheel can be thought of simply as a central solid cylinder (the part that attaches to the axle) surrounded by a thin shell of mass (the rim and tire) located along the outer edge of the wheel. Compared to these parts of the wheel, the mass of the spokes is small enough to be neglected. A sample bicycle wheel has mass 2.0 kg, half of which is in the central cylinder. The other half is in the rim and tire. The central cylinder has a radius of 4.0 cm (note the unit!). The wheel has a radius of 40.0 cm.

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

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

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

The wheel described above rolls down a ramp without slipping. It starts rolling on the ramp at a point where the ramp is 2.0 m above the ground. Any energy lost to frictional effects as the 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 have when 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. You need to set up an energy conservation equation in which you can isolate the translational velocity as the only unknown quantity.

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

Expert Solution

genius_generous answered 7 months ago

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