Phys101
Q1:
Term:122
Online HW-Ch11-Lec03
A uniform disk has radius R and mass M. When it is spinning with angular velocity ω
about an axis through its center and perpendicular to its face its angular momentum is
I com ω. When it is spinning with the same angular velocity ω about a new parallel axis
at a distance h away from COM, its new angular momentum is:
A.
B.
C.
D.
E.
I com ω
(I com + Mh2) ω
(I com - Mh2) ω
(I com +MR2) ω
(I com - MR2) ω
Ans:
B ; because ; L = Iω = (Icom + Mh2 )ω
Q2:
Two disks are mounted on low-friction bearings on a common shaft. The first disc has
rotational inertia I and is spinning with angular velocity ω. The second disc has
rotational inertia 2I and is spinning in the same direction as the first disc with angular
velocity 2ω as shown. The two disks are slowly forced toward each other along the
shaft until they couple and have a final common angular velocity ω f . If ω=21 rad/s
and I = 2 kg.m2/s, calculate ω f (in rad/s). (Give your answer in three significant
figures form)
Ans:
Conservation of Angular Momentum: Lf = Li
(I1 + I2 )ωf = I1 ωf + I2 ωf
⇒ (I + 2I)ωf = Iω + (2I)(2ω) ⇒ ωf =
=
5 × 21
= 35.0 rad/s
3
KFUPM-Physics Department
5. Iω
5ω
=
3I
3
1
Phys101
Term:122
Online HW-Ch11-Lec03
Q3:
A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600
kg.m2. It is initially spinning at 0.80 rad/s when a 20 kg child was at the center. The
child starts crawling from the center to the rim (rim means the edge). When the child
reaches the rim the angular velocity of the whole system becomes ω f . Calculate ω f (in
rad/s) of the merry-go-round. (Consider the child as point mass) (Give your answer
in three significant figures form)
𝐀𝐧𝐬:
I1 = 600 kgm2 , ωi = 0.8 rad/s; R = 3 m
child: m = 20 kg ; ri = 0 ⇒ Ii = 0
rf = R = 3 m ⇒ If = mrf 2 = 20 × 32 = 180 kg. m2
Conservation of angular momentum ∶ Lf = Li
0
⇒ (If + I)ωf = I1 ωf + Ii ωi ⇒ ωf =
⇒ ωf =
600 × 0.8
= 0.615 rad/s
600 + 180
KFUPM-Physics Department
I1 ω f
(Ii +If )
2