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Phys. 116 Final
9:0011:30 am, Dec. 16, 2003
1. (5 points) In one inertial reference frame, event A and event B occur at the same
position, with A preceding B in time. Will A precede B in all other inertial reference
frames? Explain.
2. (5 points. Dedicated to people with manualtransmission cars) Consider two disks,
rotating about a common axis, with moments of inertia I
1
and I
2
. Initially they have
rotational velocities
ϖ
1
and
ϖ
2
. Suppose that they are not subject to any external torques.
A driver then brings the two disks into contact, and they stick together. Find the final
angular velocity of the combined system.
3. (5 points) A mass on a spring is released from rest with amplitude
x
0
. Because of
viscous frictional forces, the mass does not return to its original position after one
oscillation period. Rather, its maximum displacement is reduced by a distance
∆
x
, where
x
<<
x
0
. Determine the quality factor of this oscillator using the definition
Q
=
energy stored
energy dissipated per radian
.
4. (5 points) A cart moves on a track with a constant relativistic velocity v. A and B are
observers at the two ends of the cart, and C and D are stationed along the track. We
define event AC as the occurrence of A passing C, and event BD as B passing D.
Suppose that events AC and BD are simultaneous in the cart’s reference frame. Are they
simultaneous in the track’s reference frame? If not, which event is earlier in the track’s
frame?
v
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 Fall '05
 ELSER, V
 Inertia

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