Phys101
Term:123
Online HW-Ch11-Lec01
Q1:
A solid cylinder of mass M and radius R rolls down an incline without slipping. Its
moment of inertia about an axis through its center of mass is MR2/2. At any instant
while in motion, its rotational kinetic energy about its center of mass is what fraction
of its total kinetic energy?:
A)
B)
C)
D)
E)
1/2
1/4
1/3
2/5
None of these
Ans:
C
1 2
kEr
kEr
1
2 Iω
=
=
=
2
1 2 1
MR
kETotal
kEr + kEt
Iω + 2 Mv 2
2
I +1
For solid cylinder I =
kEr
1
1
MR2 ⇒
=
kETotal
3
2
Q2:
A 240 N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is
inclined at 37ᵒ with the horizontal. What is the angular speed of the sphere at the
bottom of the slope if it starts from rest?
L
h
θ
Ans:
K i + Ui = K f + Uf
1
1
mv 2 + Iω2 = Mgh
2
2
But h = Lsinθ and I =
v = Rω
⇒
2
MR2
5
1
1 2
MR2 ω2 + � MR2 � ω2 = MgLsinθ
2
2 5
10 gLsinθ
⇒ ω= �
= 36 rad/s
7R2
KFUPM-Physics Department
1
Phys101
Term:123
Online HW-Ch11-Lec01
Q3:
A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown.
Starting from rest, the wheel moves with constant angular acceleration 6 rad/s2. The
distance traveled by the center of the wheel from t =0 to t = 3 s is:
Ans:
1
θ − θ0 = w0 t + 2 1αt 2
1
= (0)(3) + (6)(3)2 = 27 rad
2
S = rθ = 0.5 × 27 = 13.5 m
KFUPM-Physics Department
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