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HKAL Exercise : Part 1 Mechanics
Chapter 3 Circular Motion
3.1 Definition
1. The turntable of a gramophone rotates at a steady angular speed ω. A record is dropped from
rest on the turntable. Initially, the record slips but it undergoes uniform angular acceleration
and eventually moves with the same angular speed as the turntable. The turntable turns through
an angle θ while the record is slipping on its surface. Find the angular acceleration of the
record and the angle which it turns through before it attains the steady speed of the turntable.
Angular acceleration
Angle
2
A.
ω /θ
2θ
2
B.
ω /θ
θ/2
C.
D.
ω2/(2θ)
ω2/(2θ)
2θ
θ/2
B
Centripetal Force
2.
4.
H
A
A car of mass m travels into a region
where the track is an arc of a vertical
circle of radius r. At the bottom of this arc,
the car travels at speed v. At this position
the vertical force exerted upwards by the
track on the car is
A. mv2/r.
B. mg.
C. mv2/r – mg.
D. mg + mv2/r.
3.
A small object of mass 0.3 kg is released
from rest at the rim of a heavy, smooth
semi-spherical bowl of radius 25 cm. Find
the force acting on the object by the bowl
when it passes the bottom of the bowl.
A. 6 N
B. 9 N
C. 12 N
D. 15 N
HKAL Extra Exercise_Chapter 3 Circular Motion
80 m
B
40 m
Terminal
platform
The diagram shows part of the route of a
roller-coaster in an amusement park. The
cart descends from H, completes a circular
loop A and moves to B. If the cart of
passengers is to complete the central
circular track safely, what is the minimum
velocity of the cart at the bottom of the
circular track A ? (Assume that there is no
friction between the cart and the track.)
A. 24.5 m/s
B. 31.6 m/s
C. 40 m/s
D. 80 m/s
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5.
Which of the following pairs of forces
is/are example(s) of action and reaction ?
6.
(1) The forces of repulsion experienced
by two parallel wires carrying
currents in the opposite direction.
(2) The centripetal force keeping a
satellite in orbit round the earth and
the weight of the satellite.
(3) The air resistance acting on an object
falling through the air with terminal
velocity and the weight of the object.
A. (1) only
kept rotating at a constant angular speed
about a vertical axis through its centre.
The distance of B from the axis of rotation
is twice that of A from the axis. Which of
the following statements is/are correct ?
(1) The frictional force acting on B is double
that acting on A.
(2) The kinetic energy of B is double that of
A.
(3) If the angular speed of the turntable
B.
C.
D.
7.
(3) only
(1) and (2) only
(1), (2) and (3)
Two small identical coins A and B are
placed on a horizontal turntable which is
gradually increases, B will slip before A.
A. (2) only
B. (3) only
C. (1) and (2) only
D. (1) and (3) only
A student whirls a small bucket of water in a vertical circle of radius 0.7 m. For no spilling,
what is the minimum speed of the bucket at the highest point of its path ?
A. 2.65 m s-1
B. 3.74 m s-1
C.
D.
4.41 m s-1
5.29 m s-1
Whirling a ball with a string
8.
glass
tube
L
 rubber
bung

W
A student performing a centripetal force experiment whirls a rubber bung attached to one end
of a string which passes through a glass tube with smooth openings, and has a weight W
hanging at its other end. The weight of the rubber bung is much smaller than W. The rubber
bung is set into a horizontal uniform circular motion with angular speed ω while the length
of the string beyond the upper opening of the glass tube is L and this portion of the string
makes an angle θ with the vertical as shown. Which of the following statements is/are
correct ?
HKAL Extra Exercise_Chapter 3 Circular Motion
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(1) If L is kept constant, θ will increase with ω.
(2) When W increases, θ will increase.
(3) If θ is kept constant, L will increase with ω.
A.
B.
C.
D.
(1) only
(3) only
(2) and (3) only
(1), (2) and (3)
3.2 Uniform Motion in a Horizontal Circle
9.
A
25O
A.
B.
(1) only
(3) only
C.
D.
(1) and (3) only
(2) and (3) only
11.
Q
B
A smooth conical container rotates about
the axis AB as shown. A marble remains at
rest relative to the container at a radial
distance r from the axis. If the angular
velocity of the marble is ω, then ω2 is
equal to
A.
B.
C.
D.
g tan 25∘/r.
g / (r tan 25∘).
g cos 25∘/r.
g / (r cos 25∘).
10. A particle P is moving in a horizontal
circle in a clockwise direction as shown
(top view). The following diagrams show

the direction of the acceleration a of the
particle. Which of them is/are possible ?
(1)
(2)
(3)
a
P
a
P
a
v
P
A small ball-bearing is projected with
velocity v from the lowest position P of a
vertical circular track which is not smooth.
The ball-bearing starts to leave the track at
Q. Which of the following diagrams best
represents all the forces acting on the
ball-bearing at Q ?
A.
B.
Q
Q
P
P
C.
D.
Q
Q
P
P
P
HKAL Extra Exercise_Chapter 3 Circular Motion
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Conical pendulum
12. A spring of unstretched length 14.0 cm,
Level road without banking
13.
has one end fixed to the ceiling. A mass is
suspended at the other end, and the
extension so produced is 3.0 cm. When the
mass is set to rotate in a horizontal circular
path the length of the spring is 19.0 cm.
The angle between the spring and the
vertical is
A. 9∘.
B. 37∘.
C. 53∘.
D.
P
The diagram represents the rear view of a
motor car moving, away from an observer
on a level road at a constant speed around
a bend of which the centre of curvature is
at P. Which of the arrows best represents
the direction of the resultant of the forces
exerted by the road on the car?
81∘.
Banked Road
14.
A.
B.
C.
D.
15.
N
centre of mass
5m
r
A

mg
30 o
O
The figure shows a car moving round a
corner with a radius of 5 m on a banked
road of inclination 30∘. At what angular
speed would there be no friction acting on
the car along OA ?
A. 0.9 rad s-1
B. 1.1 rad s-1
C. 1.3 rad s-1
D. 1.5 rad s-1
HKAL Extra Exercise_Chapter 3 Circular Motion
A car of mass m is moving with speed v on
a banked road along a circular path of
horizontal radius r. The angle of
inclination of the road is θ . If the
centripetal force arises entirely from a
component of the normal reaction N from
the road, which of the following relations
is correct ?
A. N cos   mg
B.
v2 
gr
sin 
C.
v2 
gr
tan 
D.
N
mv 2

sin 
r
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Aircraft
16. An aircraft flies along a horizontal circle of radius 20 km with a constant angular speed of
0.012 rad s-1. Calculate the angle between its wings and the horizontal.
A. 15.0∘
B. 15.5∘
C. 16.0∘
D. 16.5∘
Bicycle on a level road
17. A motorcyclist going round a corner on a level road leans over at an angle to the horizontal.
The reason for this is
A. to lower his centre of mass.
B.
C.
D.
to provide the centripetal force.
to reduce the radius of curvature of his path.
to allow his weight to exert a torque about the contact point on the ground.
3.4 Non-Uniform Motion in a Vertical Plane
Looping the loop
18.
19.
A
P
h
A particle P is placed at a height h on a
smooth loop-the-loop track, as shown. The
radius of the loop is r. P is now released
from rest. If P is to complete the loop, the
minimum value of h should be
A. 1.5 r.
B. 2 r.
C. 2.5 r.
D. 3 r.
HKAL Extra Exercise_Chapter 3 Circular Motion
h
A ball bearing is released from rest at a
height h on a smooth track and completes
the circular loop of the track. If R is the
reaction acting on the ball bearing at the
highest point A of the loop, which of the
following graphs correctly shows the
variation of R with h ?
A.
B.
R
R
0
h 0
C.
D.
R
R
0
h 0
h
h
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Whirling freely (with a rod)
20. A stone of weight w tied to a piece of string is swung in a vertical circle. At the lowest point of
its path, the tension in the string is T and the centripetal force is F. Which of the following
statements is true ?
A. F = w + T.
B. F = w – T.
C. The net force acting upwards on the stone is F + T + w.
D. The net force acting upwards on the stone is F – T – w.
21.
O
0.7 m
P
A small object P of mass 0.4 kg is attached to one end of a light, rigid rod of length 0.7 m,
which is free to rotate about the other end O as shown. The object is swung to rotate in a
vertical circle so that it attains a speed of 4 m s-1 at its lowest position. What is the force
exerted on one end of the rod at this instant ?
A. a compressive force of 5.1 N
B. a compressive force of 13.1 N
C.
D.
a tensional force of 5.1 N
a tensional force of 13.1 N
KEY :
1 – 10 : BDBBA, DBBBC,
11 – 20 : DCCBA, CDCAB, 21 : D.
HKAL Extra Exercise_Chapter 3 Circular Motion
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