# Kolej Matrikulasi Labuan Laman Rasmi

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MATRICULATION DIVISION
MINISTRY OF EDUCATION MALAYSIA

TUTORIAL 7

TOPIC 7: ROTATION OF A RIGID BODY

1. A boy and a girl are riding on a merry-go-round which is rotating at a constant
rate. The boy is near the outer edge, and the girl is closer to the center. Who has
the greater angular displacement?

A     The boy
B     The girl
C     Both have the same non-zero angular displacement.
D     Both have zero angular displacement.

2. Which of the following statements is CORRECT for a rigid body that is rotating.

A     Its centre of rotation is its centre of mass.
B     All points on the body are moving with the same angular velocity.
C     All points on the body are moving with the same linear velocity.
D     Its center of rotation is at rest, i.e., not moving.

3. A man standing on a freely rotating frictionless platform holding two weights
with his arms extended horizontally. If he pulled the weights inward horizontally
to his chest, then the

A     angular velocity increase
B     angular velocity decrease
C     angular momentum increase
D     angular momentum decrease

4. (a)   The blades in a blender rotate at a rate of 6.5103 rpm. When the motor is
turned off the blades come to rest in 3.0 s. Calculate the angular
(b)   A pulley of radius 8.0 cm is connected by a string to a rotating motor which
is rotating at 7.0103 rad s1 and reduced to 2.0103 rad s1 in 5.0 s.
Calculate
(i) the tangential acceleration of the string,
(ii) the time taken to stop the pulley.
(Ans: 80 m s2; 2 s)

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5. (a)   A uniform solid sphere of radius 0.50 m and mass 15 kg rotates about the z
axis through its centre. Calculate its angular momentum when the angular
velocity is 3.0 rad s1.                                 (Ans: 4.5 kg m2 s1)
(b)   A figure skater increases her spin rotation rate from an initial rate of 1.0 rev
every 2.0 s to a final rate of 3.0 rev s1. Her initial moment of inertia was
4.6 kg m2.
(i) Calculate her final moment of inertia.
(ii) How does she physically accomplish this change?
(Ans: 0.77 kg m2)

6. (a)   Why is it more difficult to do a sit-up with your hands behind your head
than when your arms are stretched out in front of you?
(b)   A merry-go-round of radius 2.0 m has a moment of inertia 2.5102 kg m2
and is rotating at 10 rpm. A child of mass 25 kg jumps onto the edge of the
merry-go-round. Calculate the new angular velocity of merry-go-round.

7. An object P of mass 300 g is placed on a stationary smooth horizontal disc.
A string tied to P passes through a small hole O at the centre of the disc as shown
in FIGURE 1. P revolves about the centre with tangential linear speed of 5.0 m
s1 in a circle of radius 50 cm. The string is then pulled downwards slowly until P
travels in a circle of radius 30 cm.

P        O

FIGURE 1

(a)   Sketch the force acting on P as it travels in a circle.
(b)   Calculate the linear velocity of P in the new circle.
(c)   Calculate the total work done to reduce the size of the circle.
(Ans: 8.33 m s1; 6.66 J)

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8. A pulley of radius 20 cm has moment of inertia 0.040 kg m2 about the axis
through its centre. Part of a light string wraps round the pulley while the free
end is tied to an object of mass 2.0 kg. The object is suspended 1.5 m above the
ground and is stationary as in FIGURE 2. If the object is released, calculate its
velocity at that instant when it reaches the ground.
(Ans: 4.43 m s1)

1.5 m

FIGURE 2
9. (a)   A rotating merry-go-round makes one complete revolution in 4.0 s.
Calculate
(i) the linear speed of a child seated 1.20 m from the centre,
(ii) her acceleration.
(Ans: 1.89 m s1; 2.98 m s2)
(b)   A merry-go-round accelerates from rest to 3.0 rad s1 in 24 s. The merry-
go-round is a uniform disc of radius 7.0 m and mass 3.1104 kg. Determine
the nett torque required to accelerate it.             (Ans: 9.50104 N m)

10. A small object of mass 200 g is placed on top of one end of a uniform horizontal
rod PQ as shown in FIGURE 3. The rod has length 100 cm and moment of
inertia of 0.050 kg m2 about an axis which passes through the end P and is
perpendicular to the rod. The coefficient of static friction between the object and
rod is 0.50.                                      object

P                              Q
100 cm

FIGURE 3
Calculate the angular velocity of the rod
(a) at the moment when the object is just about to slide on the rod.
(b) immediately after the object has dropped off the rod.