7A Midterm II Sample Questions
Kevin Young
This is a list of sample problems that I will be solving for the midterm review on
Saturday, 122 in 1 Pimentel. I may not get to solve all of these in the time allotted,
and I will most likely be doing them out of order.
Problem 1  Semicircular rod
A rod of mass, m, length,
π
r, is bent into a semicircle.
1. Calculate the center of mass of the rod after it has been bent. Use symme
try considerations to reduce the problem to onedimension. I would suggest
polar coordinates for this integral.
2. Calculate the moment of inertia about an axis perpendicular to the plane of
the semicircle and passing through the point midway between the ends of the
rod. (This is like a ring spun about its center of mass, but with the bottom half
cut away)
3. Calculate the moment of inertia about and axis perpendicular to the plane of
the semicircle and through the center of mass. Don’t do any integrals for this
part.
Problem 2  Midspace Collision
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 Spring '08
 Lanzara
 Mass, Velocity

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