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5 Rotation of a Rigid Body
Objective Questions
1. The figure shows a tube X, a rod Y and another rod Z
made of different materials. All of
them have the same radius and mass. The lengths of X and Y are
the same, but Z is shorter.
The moments of inertia of X, Y and Z about their axes are
I X, I Y and
I Z respectively.
Which of the following comparisons between I X,
I Y and I Z is correct?
A I X =
I Y = I Z B I X =
I Y > I ZC I X <
I Y = I Z
D I X >
I Y = I Z
2. At the bottom of an inclined plane, the angular
velocity of a sphere of radius r is ω . The
sphere rolls up the inclined plane and stops after travelling a
distance of x . What is the angular
deceleration of the sphere?
Ar ω
2
——2 x
Br ω —– x
C 2r 2
ω
2
——– x
Dr
2ω
——2 x
3. When a constant force presses on a rotating wheel, the
wheel decelerates and finally stops.
Which of the following graphs correctly shows the variation of
the rotational kinetic energy
K of the wheel with time t ?
A C
B D
Tube X Rod Y Rod Z
K K
0 t
K
0 t
0 t
K
0 t
QB AA STPM Phys V1 C5 4th indd 1QB AA STPM Phys V1 C5 4th.indd 1
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4. Which of the following correctly explains why a person
needs to spread out his arms when
crossing a stream over a narrow beam?
A His centre of gravity is lowered.
B The base surface area is increased.
C The moment of inertia is increased.
D The torque on the person is reduced.
5. A particle of mass 2m moving with a speed
v in a circle collides into another particle of mass
m moving with an angular speed of v in the same circle, but
in the opposite direction. The
particles coalesce after collision. What is the speed of the
particles after collision?
A 0
B v
C1—2 v
D1—3 v
Structured Question
1. A uniform rod of length l and mass
M is freely hinged at one end. The other end of
the rodis raised until the rod is horizontal. The rod is then
released. When the rod is vertical, the
free end of the rod collides with a lump of plasticine which
then sticks to the rod. Both the
rod and plasticine then move off together.
Deduce the expression for the angular velocity of the rod
(a) when it is vertical
(b) after colliding with the plasticine.
[Moment of inertia of a uniform rod of length l and
mass M about the axis perpendicular
to it through one end of the rod is1—3 Ml
2.]
Essay Question
1. (a) Explain what are meant by angular
acceleration and torque produced by a force. State
the relationship between angular acceleration and torque.
(b) A wheel is accelerated uniformly from rest to an angular
speed of 32 rad s–1 during the
first 1.5 s. It is kept at this constant speed and finally
brakes uniformly to rest in the last
2.5 s. The complete cycle takes 10.0 s.
Calculate
(i) the total number of revolutions made in 10.0 s
(ii) the angular acceleration of the wheel during the
first 1.5 s
(iii) the torque on the wheel which has a moment of
inertia of 0.75 kg m2 when it is
being accelerated
(iv) the work done by the torque during acceleration.
M
l
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