1. 1
   A mechanic loosens a wheel nut using a spanner. She applies a force of 120 N to the end of the spanner, 0.30 m from the centre of the nut. The force acts in the plane of rotation at an angle of 60° to the length of the spanner. The nut does not turn.

   (a)

   What is the torque of the mechanic's force about the centre of the nut?

   [1 mark]

   • A18 N m
   • B31 N m
   • C36 N m
   • D400 N m

   (b)

   Which of the following forces, applied in the plane of rotation, would produce the same torque about the nut as the mechanic's force?

   [1 mark]

   • A104 N perpendicular to the spanner at 0.30 m from the nut
   • B120 N perpendicular to the spanner at 0.15 m from the nut
   • C60 N at 60° to the spanner at 0.30 m from the nut
   • D240 N along the length of the spanner at 0.30 m from the nut

   (c)

   Explain why the torque exerted on the nut by the thread must be at least 31 N m.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A light rod of length 0.80 m is pivoted at its centre so that it can rotate in a horizontal plane. A small 0.50 kg mass is fixed at each end of the rod. A motor applies a constant torque of 0.60 N m to the rod, which starts from rest. Friction is negligible and the masses can be treated as point masses.

   (a)

   What is the moment of inertia of the rod and masses about the pivot?

   [1 mark]

   • A0.080 kg m²
   • B0.40 kg m²
   • C0.16 kg m²
   • D0.64 kg m²

   (b)

   The masses are moved to 0.20 m from the pivot and the same torque is applied. How does the angular acceleration compare with its original value?

   [1 mark]

   • AIt is halved
   • BIt is unchanged
   • CIt is doubled
   • DIt is four times larger

   (c)

   For the original arrangement, determine the number of revolutions the rod makes in the first 4.0 s.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A potter's wheel is spinning freely with its motor disengaged. The wheel has a moment of inertia of 0.45 kg m² about its axis and an angular speed of 12 rad s⁻¹. A potter drops a 2.0 kg lump of clay vertically onto the wheel so that it sticks at a distance of 0.15 m from the axis. The clay can be treated as a point mass, and friction at the axle is negligible over the short time of the impact.

   (a)

   Determine the angular speed of the wheel just after the clay lands.

   [3 marks]

   (b)

   Compare the rotational kinetic energy of the system before and after the clay lands, and explain the difference.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A tram stores energy in a flywheel while braking and uses it to accelerate. The flywheel is a steel ring of mass 200 kg, with almost all its mass at a radius of 0.40 m, spinning about a vertical axis. At full charge it spins at 600 rad s⁻¹. A solid disc of the same mass and the same radius would have half the moment of inertia of the ring. During one acceleration the flywheel slows uniformly from 600 rad s⁻¹ to 300 rad s⁻¹ in 40 s, transferring energy to the tram's motor.

   (a)

   Determine the energy stored at full charge, the energy transferred to the tram during the 40 s, the mean power transferred, the torque acting on the flywheel and the number of revolutions it makes during the 40 s.

   [6 marks]

   (b)

   Evaluate the design of this flywheel as an energy store for a tram.

   [6 marks]

   Total for question 4: 12 marks

End of questions