IBPhysics: HLDPTopic Questions6. Circular Motion & Gravitation 6.1 Circular Motion

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First teaching 2014

Last exams 2024

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Circular Motion (DP IB Physics: HL)

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6.1 Circular Motion

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6.1 Circular Motion

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1
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In uniform circular motion, which of the following is incorrect?

  • Magnitude of the velocity is constant

  • The direction of the velocity is constant

  • The centripetal force is towards the centre of the circle

  • The centripetal force is at 90 o to the velocity

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2
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A child whirls a conker on a string around their head. The conker moves with uniform circular motion. The linear speed of the conker is 5 m s−1 and the radius of the circle is 0.5 m. 

Calculate the angular speed of the conker.

  • 2.5 rad s−1

  • 0.5 rad s−1

  • 10 rad s−1

  • 5 rad s−1

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3
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What is an angular displacement of pi over 6 rad in degrees?

  • 180 o

  • 60 o

  • 45 o

  • 30 o

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4
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The linear speed of a motorcycle of mass 50 kg on a circular race track is 10 m s−1. The radius of the race track is 500 m.

What is the centripetal force acting on the motorcycle?

  • 10 N

  • 50 N

  • 150 N

  • 100 N

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5
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An athletic hammer consists of a heavy metal ball on the end of a steel wire which is rotated around an athlete's head before being released.

The angular speed obtained by a training hammer thrown in a competition is 2 rad s−1. The combined length of the steel rope and the athlete's arms is 2 m.

What is the centripetal acceleration of the hammer?

  • 2 m s−2

  • 4 m s−2

  • 6 m s−2

  • 8 m s−2

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6
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A man is running along a circular path with an angular velocity of 0.05 rad s−1. His linear velocity is 2.5 m s−1.

What is the radius of the path?

  • 20 m

  • 30 m

  • 40 m

  • 50 m

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7
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A mass is swung on a string in a circle of radius r.

6-1-circular-motion--q7-question-sl-easy-mcq-phy

The string breaks and the mass continues to move.

Which line in the table below describes the motion of the mass in the horizontal and vertical dimensions?

 

Horizontal

Vertical
A.

Continues in a circle of radius r

No vertical motion
B.

Moves in a circle of radius > r

Moves at a constant speed downwards
C.

No horizontal motion

Decelerates downwards
D.

Moves in a straight line at 90 ° to r

Accelerates downwards

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    8
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    A ball attached to a string rotates in a gravitational field with a constant time period in a vertical plane. The forces acting on the mass are tension, T and weight, W.

    6-1-circular-motion-q8-question-sl-easy-mcq-phy

    What is an expression for the magnitude of the tension in the string at the top of the circle?

    • fraction numerator m v squared over denominator r end fraction minus m g

    • T

    • mg

    • fraction numerator m v squared over denominator r end fraction plus m g

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    9
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    A satellite moves in a uniform circular orbit around the Earth in a clockwise direction. 

    Which diagram correctly shows the direction of the velocity v and acceleration a of the satellite at the position shown?

    6-1-circular-motion-q9-question-sl-easy-mcq-phy

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      10
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      What is the force acting on an object rotating with constant speed v in a circle of radius r?

      • fraction numerator m v squared over denominator r end fractiontowards the centre of the circle

      • v squared over raway from the centre of the circle

      • fraction numerator m v squared over denominator r end fractionalong a tangent to the circle

      • No force acts on the object

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      1
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      A particle of mass m moves in a circle of radius r at uniform speed, taking time T for each revolution. What is the kinetic energy of the particle?

      • 2 m r pi f squared

      • m r squared pi squared f squared

      • 2 m r squared pi squared f squared

      • 4 m r squared pi squared f squared

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      2
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      A 0.05 kg ball is attached to an inextensible string and whirled overhead such that it rotates in a horizontal circle.

      What is the centripetal force on the ball if the string is 0.1 m long and the ball has a time period of  pi over 10s?

      • 1.0 N 

      • 0.1 N

      • 8.0 N

      • 2.0 N

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      3
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      A horizontal disc rotates uniformly at a constant angular velocity about a central axis normal to the plane of the disc.

      q13_circular-motion_ib-sl-physics-mcq

      Point X is on a distance 3L from the centre of the disc. Point Y is a distance L from the centre of the disc. Point Y has a linear speed v and a centripetal acceleration a.

      What is the linear speed and centripetal acceleration of point X?

       

      Linear Speed of X

      Acceleration of X

      A.

      3v

      a

      B.

      v

      a

      C.

      3v

      3a

      D.

      2v

      2a

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        4
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        A girl of mass 50 kg is standing on a roundabout 100 cm from the centre. The force of friction on the girl is 600 N. What is the time period if the roundabout is rotating uniformly?

        • square root of fraction numerator pi blank over denominator 6 end fraction end root

        • square root of fraction numerator 2 blank over denominator 3 end fraction end rootπ 

        • 1 thirdπ2 

        • square root of fraction numerator 1 blank over denominator 3 end fraction end rootπ 

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        5
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        A spinning top makes twenty revolutions in five minutes in a clockwise direction.

        What is the angular velocity of the spinning top?

        • fraction numerator 2 pi over denominator 15 end fraction

        • pi over 150

        • 10π

        • 1 over 15

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        6
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        A body moves in a circle with increasing angular velocity. At times t, the angles θ swept out by the body added cumulatively from the same reference point and its angular velocities ω are as follows:

        t / s

        θ / rad

        ω / rad s–1

        5

        15

        25

        35

        2

        16

        42

        80

        0.4

        2.4

        4.4

        6.4

        The angular acceleration of the body:

        • is constant at 0.2 rad s–2

        • gradually decreases and is 6.25 rad s–2 when t = 15 s

        • is constant at 0.4 rad s–2

        • increases at a constant rate and is 0.2 rad s–2 when t = 15 s

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        7
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        A hammer thrower rotates a ball on a string in a circular path gradually increasing its angular velocity with each rotation. 

        q17_circular-motion_ib-sl-physics-mcq

        When the hammer releases the ball, the subsequent path taken by the ball is

        • a vertical circle

        • a parabola in a horizontal plane

        • a parabola in a vertical plane

        • a straight line along a radius of the circle

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        8
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        An object at the end of a steel rod rotates in a vertical circle at a constant angular velocity. Which of the following statements correctly describes the tension in the rod?

        • it is greatest when the object is halfway up the circle

        • it is greatest when the object is at the bottom of the circle

        • it is unchanged throughout the motion

        • it is greatest when the object is at the top of the circle

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        9
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        For a particle moving in a circle with uniform speed, which of the following statements is incorrect?

        • The speed of the particle is constant

        • The acceleration of the particle is perpendicular to its direction of motion

        • The momentum of the particle is constant

        • The particle is accelerating

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        1
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        A particle rotates clockwise in a horizontal circle of radius r with a constant angular velocity ω. The particle is at S at time zero and at P at time t. Q represents the projection of point P onto the diameter through S. Measured with respect to the centre of orbit O, the displacement, linear velocity and linear acceleration of Q along OS are x, v and a respectively. 

        6-1-sl-mcq-hard-q1-phy

        Which of the following sets of expressions is correct? 

         

        x

        v

        a
        A.

        r space cos space omega t

        negative r omega space sin space omega t

        r omega squared space cos space omega t
        B. r space cos space omega t negative r omega space sin space omega t negative r omega squared space cos space omega t
        C.

        r space sin space omega t

        negative r omega space cos space omega t

        negative r omega squared space sin space omega t
        D.

        r space sin space omega t

        		 r omega space cos space omega t r omega squared space sin space omega t

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          2
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          A simple pendulum consists of a bob of mass m at the end of a light inextensible thread of length d. The bob swings through point Y with velocity v and comes to an instantaneous rest at point X, where the string is just taut. 

          6-1-sl-mcq-hard-q2-phy

          What is the tension in the thread as the bob passes point Y? 

          • mg

          • 2mg

          • 3mg

          • 4mg

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          3
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          A particle travels in a circular path in a magnetic field with radius x and centripetal acceleration a. 

          What is the time taken for 15 complete rotations? 

          • 2 pi square root of x over a end root

          • 30 pi square root of x over a end root

          • 2 pi square root of a over x end root

          • 30 pi square root of a over x end root

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          4
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          A mass m1 is attached to one end of a light extensible string of length x. When the mass rotates with a linear speed v in a horizontal plane, an extension Δx is obtained. 

          Which of the following shows the correct expression for another mass m2, if it is attached to the same light extensible string and rotated with the same linear speed v but rotates at twice the radius as that produced by m1?

          • m subscript 2 equals fraction numerator 2 m subscript 1 left parenthesis x plus increment x right parenthesis over denominator increment x end fraction

          • m subscript 2 equals fraction numerator 2 m subscript 1 left parenthesis 2 x plus increment x right parenthesis over denominator increment x end fraction

          • m subscript 2 equals fraction numerator 4 m subscript 1 left parenthesis x plus increment x right parenthesis over denominator increment x end fraction

          • m subscript 2 equals fraction numerator 2 m subscript 1 left parenthesis x plus 2 increment x right parenthesis over denominator increment x end fraction

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          5
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          Two bobs A and B, of equal mass, are connected by a light inextensible string of length l. 

          6-1-sl-mcq-hard-q5-phy

          Bob A is tied to a nail at the centre of a smooth table by another light, inextensible string of length 3l. The bobs are then set into uniform motion on the surface of the table with the same angular velocity. 

          What is the ratio of the tension in the string connecting bob A and B to that in the string connecting bob A to the nail? 

          • 1:2 

          • 3:4 

          • 4:7

          • 4:9

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          6
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          An aircraft moves in a horizontal plane at a constant linear speed v and makes a turn of radius r. 

          6-1-sl-mcq-hard-q6-phy

          Which of the following expressions is true for the tilt angle θ?

          You may wish to use the relationship:

          tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction

          • theta proportional to r

          • theta proportional to 1 over r

          • tan space theta proportional to r

          • tan space theta proportional to 1 over r

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          7
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          The maximum speed for a car to safely move round a corner when the road is dry is 10 m s–1. The maximum frictional force between the road surface and the wheels of the car is halved when the road is wet. 

          What is the maximum safe speed for a car to go round the corner when the road is wet? 

          • square root of 2 m s–1

          • 2 square root of 2 m s–1

          • 5 square root of 2 m s–1

          • 10 square root of 2 m s–1

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          8
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          A conker attached to a string is whirled in a vertical circle at constant speed. 

          Which of the following correctly shows the variation of the tension T in the string with the angular displacement θ? 

          6-1-sl-mcq-hard-q8-phy

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            9
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            A small object is attached to a string and whirled in a vertical circle at a constant speed. The magnitude of the net force F on the object at the top of the circle is given by:

            F subscript t o p end subscript space equals space T space plus space m g

            Where T is the tension in the string, m is the object's mass and g is the acceleration of free fall.

            The magnitude of the net force on the object at the bottom of the circle is given by: 

            F subscript b o t t o m end subscript space equals space T space minus space m g

            Which of the following statements is correct?

            • The net force on the object at the bottom of the loop is greater than the net force at the top

            • The net force on the object decreases as the object moves from the bottom to the top of the loop

            • The net force on the object at the top of the loop is greater than the net force at the bottom

            • The net force on the object is the same at the top and at the bottom of the loop

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            10
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            Two masses m1 and m2 are fixed on a horizontal circular rotating platform. m2 is half as massive as m1 and is fixed at a distance three times as far from the centre as m1. The net force on m1 is F1 and the net force on m2 is F2.

            Which of the following statements is correct? 

            • F subscript 1 equals 1 half F subscript 2 

            • F subscript 1 equals 1 third F subscript 2

            • F subscript 1 equals 2 over 3 F subscript 2

            • F subscript 1 equals 2 F subscript 2

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