PHY2053 F23 Quiz 6_V3_solutions (1)
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PHY2053 QUIZ 6
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Name: ___________________
Section Number
2
1.
A newly fabricated nanotube of radius r m rolls down onto a substrate and decelerates due to the friction (no slip). Suppose the nanotube decelerates at a
t
m/
s
2
and finally comes to rest after N revolutions and it has a radius of r m. What is the initial angular velocity of the nanotube, in terms of a
t
, N, r?
With
−
a
t
=
αr
0
2
−
ω
i
2
=
2
α ∆ θ
N
=
∆θ
2
π
We have
ω
i
=
√
2
a
t
/
r ×
2
πN
=
√
4
πN a
t
/
r
3
Name: ___________________
UFID:
Section Number
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2.
You are an alien playing with a CD mounted on a CD player (both the player and the CD are products of your planet but somehow the CD is still in the shape of a disk). Suppose you exert a force of 150 N tangential
to the outer edge of the CD, which has a mass of 75 kg, and cause the CD an angular acceleration of 3.2 rad/
s
2
. If the friction between the CD and the player can be neglected, what is the radius of the CD, in meter?
With
τ
=
FR
τ
=
Iα
I
=
1
2
m R
2
We have
R
=
F
1
2
mα
=
150
N
1
2
(
75
kg
)(
3.2
rad
s
2
)
=
1.25
m
4
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