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Unformatted text preview: Review for Exam 1 Exam 1
• Next Monday during class
• Covers up to C9
• 3 problems, 33 points each
• No calculator or notes
• Formula sheet will be provided
• Be on time! Formula Sheet
Velocity: dr
dt
= vAB + vCD v=
vAC
Momentum and center of mass: 1
(m1 r1 + m2 r2 + · · ·) ,
M
p = M vcm
dp
Fnet =
dt M = m1 + m2 + · · · rcm = Energy:
E =K +V
K = 1 mv 2
2
dV
dx
GM m
=−
mgh + const
r
= 1 k (r − r0 )2
2 Fx = −
Vgrav
Vspring dE = Fnet · dr
Rotation:
v = ω r,
Krot = 1 I ω 2 ,
2 2
m i ri = I= 2
2
Krot cm = 1 M vcm + 1 I ωcm
2
2 i dm r 2 What the *&$#!
does this mean? Problem 1: Two balls with equal mass m are suspended from a light string of
length L. One of the balls is pulled to the left by an initial angle θ and then
released from rest. When it collides with the other ball, the two balls stick
together and move to the right.
(a) (10 points) During what part of this process is momentum conserved?
During what part of this process is energy conserved? Explain.
(b) (23 points) Find the maximum height of the two balls after the collision. M
θ
F Problem 2: A wheel of mass M and radius R on a horizontal surface is initially
at rest. A constant force F then begins to pull on the axle of the wheel at an
angle θ below the horizontal. The wheel rolls without sliding until it travels a
horizontal distance d.
The moment of inertia of the wheel is
(a) (15 points) How much does the energy of the wheel change during this
process?
(b) (18 points) What is the speed of the wheel at the end of this process? shown below. Compute the moment of inertia of the rod for this kind of rotation. Does your answer
makes sense as θ33 points) A rod of mass M and length L rotates about an axis that
Problem 3: ( → 0? makes an angle θ with the rod, as shown. Find the moment of inertia of the rod
for this kind of rotation. ...
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 Fall '10
 MarkusLuty
 Physics, Center Of Mass, Mass, Momentum

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