The questions are on the rotational inertia test. Take it under real conditions before reading the mark scheme.
Quick answer: Rotational inertia I measures how strongly an object resists changes in its rotation and depends on both mass and how far that mass is from the axis. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 1 test on rotational inertia, from definition to hoop or disk, with the equivalent answers to accept.
Model answers with the mark scheme. Give credit for a correct equation or substitution even if the arithmetic slips, and apply the unit mark in each calculation.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 5
Question 1 Definition (2 marks)
a. Rotational inertia is a measure of an object’s resistance to changes in its rotational motion about a given axis, I = Σmr².
b. Any two of: its mass; the distribution of the mass (distance from the axis); the position of the axis.
Marking: 1 mark for each part.
Question 2 Three point masses (3 marks)
a. I = Σmr² = 0.20 × (0.10)² + 0.30 × (0.20)² + 0.50 × (0.40)² = 0.0020 + 0.012 + 0.080 = 0.094 kg m².
b. The 0.50 kg mass contributes most (0.080 kg m²): it is both the heaviest and the farthest from the axis, and r is squared.
Marking: (a) 1 mark for the method, 1 mark for the result; (b) 1 mark.
Question 3 Wheel on an axle (2 marks)
a. τ = rF = 0.30 × 12 = 3.6 N m.
b. α = τ/I = 3.6 ÷ 0.25 = 14 rad/s² (14.4).
Marking: 1 mark each, with units.
Question 4 Pulley and hanging mass (3 marks)
a. I = ½MR² = 0.0050 kg m²; T = Ia/R² = ½Ma = 0.50a. mg − T = ma gives 0.50 × 9.81 = (0.50 + 0.50)a, so a = 4.9 m/s².
b. T = 0.50 × 4.905 = 2.5 N.
Marking: (a) 1 mark for the two equations, 1 mark for the result; (b) 1 mark.
Question 5 Swinging a bat (3 marks)
Holding the bat at the end puts the heavy part far from the axis, so its rotational inertia I = Σmr² is large. By τ = Iα, the same torque from the hands gives a smaller angular acceleration. Holding it nearer the heavy part reduces r, hence I, so the bat speeds up more easily.
Marking: 1 mark for relating I to distance, 1 mark for τ = Iα, 1 mark for the conclusion about α.
Question 6 Pushing a door (2 marks)
a. τ = rF sinθ = 0.80 × 30 × sin 60°.
b. τ = 24 × 0.866 = 21 N m (20.8).
Marking: 1 mark each.
Question 7 Accelerating a wheel (3 marks)
a. α = Δω/t = 30 ÷ 5.0 = 6.0 rad/s².
b. I = τ/α = 0.60 ÷ 6.0 = 0.10 kg m².
c. θ = ½αt² = ½ × 6.0 × (5.0)² = 75 rad.
Marking: 1 mark each.
Question 8 Hoop or disk (2 marks)
The disk has the larger angular acceleration. Ihoop = MR² and Idisk = ½MR², so with the same torque α = τ/I is 2 times greater for the disk.
Marking: 1 mark for naming the disk with reference to I; 1 mark for the factor of 2.
