Summer 2008 – third midterm
 two pages/sides
Attempt in any order
ALWAYS GIVE YOUR REASONING
(1)
(a)
what is the momentary velocity (speed and direction) of the piece of
rubber on the very front
of a bicycle wheel when the bicycle is travelling at
10m/s?
the bottom of the wheel is momentarily stationary, and the wheel rotates about it.
the distance from the bottom of the wheel to the front is
2
times the distance to
the hub, which is travelling at 10. so the answer is
10
2
the same answer can be obtained by adding the linear motion forward to the
rotation around the axle hub.
(b)
a solid iron sphere of mass 1kg rolls down a 30 degree slope, for a
distance of 2 meters.
find its speed as it reaches the bottom.
The moment of
inertia of a sphere is
I
=
2
5
MR
2
height lost = 1 meter, so p.e. lost = 1(1g) =10 approx.
this appears as linear +
rotational kinetic energy. with M the total mass,
mgh
≈
10
=
1
2
mv
2
+
1
2
I
ω
2
=
1
2
mv
2
+
1
2
2
5
mR
2
⎛
⎝
⎜
⎞
⎠
⎟
ω
2
=
7
10
mv
2
as v
=
mR
with m
=
1,
v
=
10
7
by coincidence (g~9.8) this is also nearly
14
(2)
(a)
can a ladder lean against a wall if there is a high coefficient of friction
at the wall, but the floor itself is perfectly smooth? say why or why not.
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 Spring '08
 Lanzara
 Physics, Friction, Mass, 1g, 1 meter, Everest

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