IBPhysicsHLTopic QuestionsSpace, Time & MotionRigid Body Mechanics

Syllabus Edition

First teaching 2023

First exams 2025

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Rigid Body Mechanics (HL IB Physics)

Topic Questions

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1
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Two co-planar forces of equal magnitude F act on the rim of a wheel.

Which pair of forces act as a couple on the wheel?

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2
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Three statements about rotational equilibrium are:

  1. There is a resultant force acting on the system
  2. There is no resultant torque acting on the system
  3. The system rotates with a constant angular velocity

Which statements about rotational equilibrium are correct?

  • I and II only

  • I and III only

  • II and III only

  • I, II and III

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3
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Which equation links linear displacement and angular displacement? 

  • s space equals space u t space plus space 1 half a t squared

  • v space equals space r omega

  • s space equals space r theta

  • a space equals space minus omega squared x

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4
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At the beginning of a wash cycle, a washing machine drum makes its first full revolution from rest in 0.05 seconds.

What is the rotational velocity of the drum after one full revolution? 

  • 1 halfπ rad s−1

  • 1 over 10π rad s−1

  • 40π rad s−1

  • 80π rad s−1

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5
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A rigid rod is rotated about different axis of rotation from different positions along the rod. The axis of rotation is indicated by a straight line and the direction of rotation with an arrow. 

9-2-e-1b-moments-rod-rotating

Which of the following rods is the hardest to rotate? 

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1
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A swinging clock pendulum is 12 cm long with a bob of mass 5 g. The linear acceleration of the swing is 4.2 m s−2.

What is the torque acting on the pendulum bob during this motion? 

  • 7.2 × 10−5 N m

  • 3.024 × 10−4 N m

  • 2.52 × 10−3 N m

  • 252 N m

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2
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A record with a radius of 17 cm and a mass of 150 g is being played on a turntable at a rate of 35 revolutions per minute.

Calculate the resultant torque on the record when it is played for 30 seconds. 

  • 5.3 × 10−4 N m

  • 5.06 × 10−3 N m

  • 1.59 × 10−2 N m

  • 0.25 Nm

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3
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A car has four wheels each of diameter 50 cm and mass 28 kg. As the car drives along a flat horizontal road, each tire moves with a linear velocity of 14 m s−1. 

What is the total rotational kinetic energy of the top point of all four tires?

  • 98 J

  • 686 J

  • 2744 J

  • 10976 J

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4
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A wind-up toy ballerina statue starts unwinding by rotating at 3 revolutions per minute about a pivot at its feet. During the unwinding, the ballerina rotates 360π radians and has a radius of rotation of 25 cm from its pivot. The ballerina maintains a constant linear acceleration of 1.75 × 10−4 m s−2 as it unwinds.

How many minutes does it take the ballerina to unwind?

  • 20

  • 23

  • 30

  • 1404

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5
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A car wheel of mass 12 kg is manoeuvred on the floor by attaching two identical solid cylinders each of mass 4 kg, length 15 cm and diameter 5 cm either side of a fastening in the centre of the wheel. The outside of the wheel is made up of a solid rim and tire with a radius of 30 cm from the centre of the tire. The inside of the tire with the spokes and fastening is modelled as an empty space with a radius of 20 cm from the centre. 

Moment of inertia of a solid cylinder rotated through the centre of the circular face: I space equals space 1 half m R squared where R is the radius of the circle

Moment of inertia of a cylinder with an empty centre: I space equals space 1 half m open parentheses A squared plus B squared close parentheses where A is the radius of the empty centre and B is the radius of the entire circle

rigid-body-mechanics-mcq5h

What is the overall moment of inertia of this system? 

  • 0.2675 kg m2

  • 0.7813 kg m2

  • 0.7825 kg m2

  • 0.7900 kg m2

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1
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A student holds a pencil horizontally by the tip and lets it swing down to a vertical position. The pencil is 8 cm long and there is a 2 g mass of blu-tac stuck on the end that swings. 

What is the moment of inertia acting on the bluc-tac during this motion? 

  • 1.28 × 10−5 kg m2

  • 1.6 × 10−4 kg m2

  • 123 kg m2

  • 128 kg m2

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2
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A boy of mass 55 kg is bouncing on a trampoline. When he does a somersault he tucks up into a ball so his whole body is no more than 67 cm away from his centre of mass. During his somersault, he rotates with a linear velocity of 7.1 m s−1.

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What is the boy's angular momentum during the somersault?

  • 175 kg m2 rad s−1

  • 262 kg m2 rad s−1

  • 391 kg m2 rad s−1

  • 2.62 × 106 kg m2 rad s−1

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3
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A ceremonial pole of length S is being held by two performers. One performer is holding each end. Both performers are applying a force of 15 N at an angle of 60° to the pole. The total torque applied by the couple on the pole is 45 N m. 

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What is the length of the ceremonial pole S ?

  • square root of 3N m

  • 3 N m

  • 2 square root of 3 N m

  • 4 square root of 3 N m

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4
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A rod is fixed to a pulley. Two 50 N forces are applied to the ends of the rod as shown. The tension in the rope attached to the pulley is T. The system is in equilibrium.

q5-paper-1-june-2018-ocr-a-level-physics

What is the value of the tension in the rope?

  • 40 N m

  • 100 N 

  • 150 N

  • 200 N

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5
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A CD of radius 60 mm rotates at a rate of 500 revolutions per minute. 

What is the linear acceleration of the CD when it rotates for 3 minutes?

  • 0.0174 m s−2

  • 0.167 m s−2

  • 0.29 rad s−2

  • 62.8 m s−2

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