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WorksheetsMotion in a Circle
Total questions: 43
Worksheet time: 43mins
A powerful laser beam, with a very small divergence angle θ, is pointed at the Moon, a distance R away.
The value of R is in kilometres and the angle θ is in degrees.
Which of the following expressions gives the diameter, in metres, of the circle of light the laser produces on the Moon?
1.75 x 10-5 Rθ
1.75 Rθ
1000 Rθ
5.73 x 104 Rθ
A particle moves through a circular arc of length l and radius r in time t. Which expression gives its angular velocity about the centre of the circle?
1 / rt
r / lt
2π / lt
2πr / t
The axis of rotation of a circular plate is through its centre and perpendicular to its plane. Two particles P and Q are on the plate. The distance P from the axis is twice that of Q.
At a given instant what is the value of (the linear velocity of P) / (the linear velocity of Q) ?
4
2
1/2
1/4
A communication satellite is moving at constant speed in a circular orbit about the Earth.
Which row in the table is correct about the momentum and kinetic energy of the satellite?
A
B
C
D
Which statement is correct about a particle moving in a horizontal circular path with constant angular velocity?
The linear momentum is constant but the kinetic energy varies
The kinetic energy is constant but the linear momentum varies
Both kinetic energy and linear momentum are constant
Both speed and linear velocity are constant
A body is moving in uniform circular motion.
Which row in the table correctly describes the linear velocity, angular velocity and linear acceleration of the body?
A
B
C
D
What is the mean angular speed of the minute hand of a clock?
1.4 x 10-4 rad s-1
1.7 x 10-3 rad s-1
5.2 x 10-3 rad s-1
1.0 x 10-1 rad s-1
A tape leaves a spool at a constant speed v and at a variable distance r from the centre of the spool.
How is the angular velocity of the spool related to r?
It is proportional to 1 / r2
It is proportional to 1 / r
It does not depend on r
It is proportional to r
A compact disc is rotating in a disc drive at a constant number of revolutions per second. A point on the disc, a distance r from the centre of rotation, is moving with speed v.
Which of the following graphs best illustrates the relationship between v and r?
The given diagram illustrates a cylinder of radius 10.0 cm rolling at a constant angular velocity of 3/4 π rad s-1 along a surface from left to right. The point X is initially at the bottom of the cylinder.
After 4.00 s, what is the displacement of X?
0.020 m
0.150 m
0.942 m
0.963 m
The given diagram shows a straight length of tape being wound on to a reel. The reel is rotating about a fixed axis with constant angular velocity and its radius is increasing at a steady rate.
Which graph correctly shows the variation with time of the speed v at which the tape moves towards the roll?
An object is travelling in a circular path with increasing angular velocity. The given table shows the angles θ swept out by the object and its angular velocities ω at various times t.
What is the angular acceleration of the body?
gradually decreases and is 4.5 rad s-2 when t = 6 s
is constant at 4 rad s-2
is constant at 8 rad s-2
increases at a constant rate and is 15 rad s-2 when t = 6 s
A spacecraft is moving in a circular orbit around the Earth when its engine is fired and produces a force on the spacecraft exactly equal and opposite to that exerted by the Earth's gravitational field.
How would the spacecraft move?
along a spiral path towards the Earth's surface.
along the line joining it to the centre of the Earth (i.e. radially)
along a tangent to the orbit
in a circular orbit with a longer period
An engine has a component rotating at 3000 revolutions per minute in a circle of radius 8.0 cm.
Which of the following is its centripetal acceleration?
25 m s-2
7900 m s-2
3.1 x 104 m s-2
7.2 x 107 m s-2
An oscillating pendulum bob of mass 1.27 kg is suspended from a string of length 0.600 m. At the instant when the string is vertical, it is moving with a velocity of 0.575 ms-1 horizontally.
Which of the following is the tension in the string at this instant?
11.8 N
12.5 N
13.2 N
13.7 N
A swinging pendulum bob of mass m and weight W is suspended from a string of length r. At the instant when the string is vertical, tension in the string is T and the bob is moving at speed v.
Which of the following expressions relating W and T is correct?
T = W
T - W = v2 / r
T - W = mv2 / r
W - T = mv2 / r
The given diagram illustrates Singapore on the Equator and Cambridge at a latitude of 52° N.
Due to the Earth's rotation about its axis, a person in Singapore experiences a centripetal acceleration of a(s) while another person at Cambridge experiences a centripetal acceleration of a(c).
The radius of the Earth may be taken as 6.4 x 106 m, and its angular velocity about its axis may be taken as 7.3 x 10-5 rad s-1.
Which row of the table shows the correct magnitudes of the centripetal accelerations?
A
B
C
D
When the road is dry, the maximum safe speed of a car moving on a unbanked circular road is 20 ms-1. When the road is wet, the maximum frictional force between the road surface and the wheels of the car is halved.
What is the maximum safe speed of the car on the circular road when it is wet?
An object travels with constant speed in a circular path of radius r. If it takes time T to complete one revolution, which row in the given table shows the correct magnitudes for its angular velocity ω, its linear velocity v, and its acceleration a?
A
B
C
D
A boy sitting on a roundabout is moving with uniform speed in a horizontal circular path. The boy's velocity and acceleration as well as the resultant horizontal force acting on the boy are all vectors.
Which of the following diagrams correctly illustrates the directions for these vectors?
A body is moving with speed v and angular velocity ω in a circle of radius r.
What is its centripetal acceleration?
rω
vω
v / r
v2 / r
The given diagram shows a steel ball fixed to one end of a light rod which rotates in a vertical circle with a constant speed.
Which of the following graphs could represent how the tension T in the rod varies with angle θ?
A body of mass 2 kg moves with a constant speed in a horizontal circle of radius 5 m. If one complete revolution takes 3 s, what is the magnitude of the resultant force acting on the body?
A body moves with constant speed around a circle of radius 1.0 m in 1.0 s.
What is the magnitude of its acceleration?
zero
10 ms-2
2 π ms-2
4 π2 ms-2
The given diagram shows a ball of mass 0.10 kg attached to a string and swung in a vertical circle of radius 0.50 m. At the top of the circle, its speed is 6.0 ms-1. [The value of g may be taken as 10 ms-2]
What is the tension in the string at this moment?
10 N
6.2 N
7.2 N
8.2 N
A body is moving at constant speed v in a circular path of radius r. What are the magnitudes of its tangential acceleration and centripetal acceleration?
A
B
C
D
A weather satellite of mass m is moving at constant angular speed ω in a circular orbit of radius r about the Earth's centre of mass.
Which expression gives the work done on the satellite in one revolution?
zero
2 π m r2 ω2
π m r2 ω2
m r2 ω2
A cyclist is making a left turn on a rough road surface at constant speed v. The bicycle and the rider are inclined to the left, as shown. The point G is the combined centre of gravity of their total mass m. The resultant of the normal reaction and the frictional force is R.
Which of the following vector diagrams correctly shows the directions of the forces acting on the bicycle and the rider?
Each diagram below shows an instant of a pendulum bob moving in a horizontal circle with constant angular speed. Which diagram correctly shows the direction of the resultant force acting on the bob?
A Concorde aircraft is moving at a constant speed of 650 ms-1 in a horizontal circle of radius 80 km.
What is the ratio centripetal force / weight of aircraft?
8.3 x 10-4
0.54
1.9
52
A motor-cyclist with sufficient speed is able to move in a horizontal circle on the inside surface of a vertical cylindrical wall.
The diagrams below are vertical sections showing the motor-cyclist and the forces acting at any instant. In the diagrams, F is a frictional force, W is the total weight of rider and motor-cycle, N is the normal reaction of the surface on the motor-cycle, and P is an outward force.
Which diagram shows the correct orientation for the cyclist, and the directions for the force acting?
A car is travelling at a constant speed v over a humpback bridge with radius of curvature r.
The car of mass m remains in contact with the road and exerts a net force R on the road when it is at the top of the bridge. Which expression gives the correct value for R?
The given diagram shows a wheel of mass m with a centre of mass G which is not its geometrical centre O. The wheel is mounted on bearings with its axle horizontal and rotates about its centre O with constant angular velocity ω.
Which graph most correctly shows the variation of the downward thrust T on the bearings as the wheel rotates through one revolution?
A particle of mass 0.050 kg is attached to one end of an elastic cord of unstretched length 0.50 m. The force constant (i.e. the force required to produce unit extension) of the elastic cord is 40 N m-1.
The given diagram illustrates the particle moving on a smooth table in a horizontal circle of radius 0.70 m.
What is the approximate speed of the particle?
11 ms-1
15 ms-1
20 ms-1
24 ms-1
An aircraft is moving at constant speed in a horizontal circular path with centre Q. The diagrams below show tail views of the aircraft with the circle representing the centre of gravity of the aircraft and the dotted line representing the line of the wings.
Which diagram correctly shows the forces acting on the aircraft?
A pendulum is hung from the roof of a railway carriage. A student sits in the carriage facing the direction in which the train is travelling. The pendulum is directly in front of him.
The train is moving in a circular path bending to the right.
Which diagram correctly shows the position of the pendulum as seen by the student and the directions of the forces acting on it?
The given diagram shows a particle of mass m moving with constant speed v in a horizontal circle of radius r. For the movement from X to Y (where XY is a diameter), which row in the table correctly gives (i) the work done by the centripetal force, (ii) the change in linear momentum of the body?
A
B
C
D
When a body is moving in a horizontal circular path with a constant speed, a centripetal force F is applied to it.
If the same centripetal force is applied while the radius of the circular path is reduced, what would happen to the speed and the angular frequency of the body?
A
B
C
D
A car of mass m is moving with speed v in a horizontal circle of radius r on a banked curve, as shown.
The normal force on the car from the road surface is N and the road surface is inclined at an angle θ to the horizontal.
Given that a component of N provides the required centripetal force, which of the following expressions is correct?
N cosθ = mg
N = mg cosθ
v2 = g r / sinθ
v2 = g r / tanθ
When a car rounds a curve of radius r at speed v, the required centripetal force on the car is F. If the car rounds the same curve at speed 2v, what is the required centripetal force?
1/2 F
F
2F
4F
A segment of the rollercoaster track in an amusement park is as illustrated.
In this segment, the carriage descends from rest at H, moves through a vertical loop with its top at A, and then over a hump at B. The friction between the carriage and the track may be taken as negligible.
If the carriage is to complete the loop without leaving the track, what is the minimum value of the height y?
23 m
25 m
27 m
30 m
Which statement explains why the Moon stays in its orbit at a constant distance from the Earth?
The gravitational pull of the Earth on the Moon is just sufficient to cause the centripetal acceleration of the Moon
The gravitational pull of the Earth on the Moon balances the gravitational pull of the Moon on the Earth.
The gravitational pull of the Moon on the Earth is negligible at this distance.
The centripetal force the Earth exerts on the Moon balances the centripetal force the Moon exerts on the Earth.
For satellites in circular orbits around the centre of the Earth, which of the following expressions gives the correct relationship between their speeds v and the radii r of their orbits?
v ∝ r2
v ∝ r
v2 ∝ 1 / r
v ∝ 1 / r2
