Rolling Objects
In this exercise you will compare the rolling speeds of several round objects down an
incline.
Preliminary questions
1. Two solid spheres have the same radius but have different masses. If they are
simultaneously released from rest at the top of an incline, which will reach the bottom
first? Explain the reason for your answer.
2. Now suppose that the two solid spheres have the same mass but have different radii.
Which will reach the bottom first? Explain.
3. If a hoop and a disk have the same mass and radius, which will reach the bottom of
the incline first? Explain.
Exercise
1. Pick two objects that have the same shape but different radii and/or different masses.
Place them side-by-side on the incline and release them from rest at the same time.
How does the speed depend on the radius? On the mass?
2. Now compare the rolling speeds of objects of different shapes (cylindrical shell, solid
cylinder, spherical shell, solid sphere). What are your results?
Analysis of Results
1. Are your experimental observations in agreement with your answers to the
preliminary questions? Explain.
2. Assume that the rotational inertia of a round object can be written as I = kMR2, where
k is a shape factor. Derive a general expression for the speed of the object in terms of
k and the initial height,.h.
3. Examine the equation that you derived above. What does it say about the dependence
of the speed on the mass? On the radius? On the shape factor (k)?
4. How would you design a rolling object that was faster than any of the ones that you
have used here?