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Rigid Body Mechanics (DP IB Physics: HL): Exam Questions

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Rigid Body Mechanics

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11 mark

Two forces, each of magnitude F, act on the rim of a wheel.

Which pair of forces forms a couple?

q7_moments_aqa-as-physics-mcq

    Choose your answer

    21 mark

    Three statements about rotational equilibrium are:

    I. There is a resultant force acting on the system

    II. There is no resultant torque acting on the system

    III. 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

    Choose your answer

    31 mark

    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

    Choose your answer

    4
    Sme Calculator    1 mark

    At the beginning of a wash cycle, the drum of a washing machine rotates with constant angular acceleration and makes its first full revolution from rest in 0.05 seconds.

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

    • straight pi over 2 rad s−1

    • straight pi over 10 rad s−1

    • 40 straight pi rad s−1

    • 80 straight pi rad s−1

    Choose your answer

    51 mark

    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? 

    rigid-body-mechanics-mcq5e-ib-hl-physics

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      1
      Sme Calculator      1 mark

      A uniform rod of length 0.80 m is at rest on a horizontal surface. The rod is pivoted so that it is free to rotate about a vertical axis through one of its ends. A particle of mass 0.25 kg collides with and sticks to the other end of the rod.

      The moment of inertia of the rod about the axis is 0.32 kg m2.

      What is the moment of inertia of the rod–particle system?

      • 0.16 kg m2

      • 0.36 kg m2

      • 0.48 kg m2

      • 0.52 kg m2

      Choose your answer

      2
      Sme Calculator      1 mark

      A person of mass M bounces on a trampoline and performs a series of manoeuvres. In the first manoeuvre, the person performs a somersault by tucking into a ball of radius R and rotating at constant angular speed omega about an axis at their centre. The angular momentum of the person is L.

      rigid-body-mechanics-mcq2m-ib-hl-physics

      In the second manoeuvre, the person performs a vertical twist by straightening their body into a cylindrical shape of radius R over 2 and rotating at constant angular speed 2 omega about an axis through their centre.

      The moment of inertia of a solid sphere of mass m and radius r is 2 over 5 m r squared.

      The moment of inertia of a cylinder of mass m and radius r is 1 half m r squared.

      What is the angular momentum of the person during the second manoeuvre?

      • fraction numerator 5 L over denominator 8 end fraction

      • fraction numerator 5 L over denominator 4 end fraction

      • fraction numerator 5 L over denominator 2 end fraction

      • 5 L

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      3
      Sme Calculator      1 mark

      A ceremonial pole of length S is held by two performers, with one at each end. Each performer applies a force of 15 N at an angle of 60° to the pole. The resultant torque exerted on the pole is 45 N m. 

      4-1-3d-e-torque-angled-forces

      What is the length S of the ceremonial pole?

      • square root of 3 space straight m

      • 3 space straight m

      • 2 square root of 3 space straight m

      • 4 square root of 3 space straight m

      Choose your answer

      4
      Sme Calculator      1 mark

      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

      Choose your answer

      5
      Sme Calculator      1 mark

      A disc of radius 60 mm is made to rotate by applying a constant force to its outer rim. It takes 3.0 seconds for the disc to rotate from rest up to an angular frequency of 500 revolutions per minute.

      During the application of the force, what is the linear acceleration at a point on the outer rim of the disc?

      • straight pi over 3 space straight m space straight s to the power of negative 2 end exponent

      • straight pi space straight m space straight s to the power of negative 2 end exponent

      • fraction numerator 10 straight pi over denominator 3 end fraction space straight m space straight s to the power of negative 2 end exponent

      • fraction numerator 50 straight pi over denominator 9 end fraction space straight m space straight s to the power of negative 2 end exponent

      Choose your answer

      1
      Sme Calculator      1 mark

      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 at the amplitude of the swing? 

      • 7.2 × 10−5 N m

      • 3.0 × 10−4 N m

      • 2.5 × 10−3 N m

      • 2.5 × 102 N m

      Choose your answer

      2
      Sme Calculator      1 mark

      A record of mass M and radius R rotates on a turntable at a constant rate of 30 revolutions per minute.

      The turntable motor is then switched off, and a braking system applies a constant torque, bringing the record to a complete stop in 3.0 seconds.

      The moment of inertia of the record is 1 half M R squared.

      What is the magnitude of the resultant torque that acts on the outer rim of the record as it comes to a stop?

      • 1 over 6 M R squared

      • straight pi over 6 M R squared

      • 3 over 2 M R squared

      • fraction numerator 3 straight pi over denominator 2 end fraction M R squared

      Choose your answer

      3
      Sme Calculator      1 mark

      A car has four wheels, each modelled as a disc of diameter 50 cm and mass 28 kg. The wheels roll without slipping as the car drives along a flat horizontal road. The centre of mass of each wheel moves with a linear velocity of 14 m s−1.

      The moment of inertia of a disc of mass m and radius r about an axis through its centre is 1 half m r squared.

      What is the total kinetic energy of the wheels?

      • 1.1 cross times 10 squared space straight J

      • 4.5 cross times 10 squared space straight J

      • 2.9 cross times 10 cubed space straight J

      • 1.1 cross times 10 to the power of 4 space straight J

      Choose your answer

      4
      Sme Calculator      1 mark

      A tetherball is suspended from the top of a vertical, stationary pole by a rope of negligible mass, as shown. The ball, which can be modelled as a point mass, is given an initial linear speed v, and the rope starts to wrap around the pole.

      Diagram of a swinging ball attached to a pole with a string, moving in a circular path. The radius of the circle is labeled r, and velocity is represented by v.

      What is the linear speed of the ball when the rope has become wrapped around the pole such that the distance between the ball and the pole has been reduced by half?

      • 1 fourth v

      • 1 half v

      • 2 v

      • 4 v

      Choose your answer

      5
      Sme Calculator      1 mark

      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 a disk with an empty space of radius 20 cm from the centre. 

      The moment of inertia of a solid cylinder about an axis through its centre is 1 half m R squared, where R is the radius of the cylinder.

      The moment of inertia of a disk with an empty centre is 1 half m open parentheses A squared space plus space B squared close parentheses, where A is the inner radius of the disk, and B is the outer radius of the disk.

      rigid-body-mechanics-mcq5h

      What is the total moment of inertia of the system?

      • 0.2675 kg m2

      • 0.7813 kg m2

      • 0.7825 kg m2

      • 0.7900 kg m2

      Choose your answer