QUESTION PAPER 1

Chapter 6: System of Particles and Rotational Motion

Original chapter-specific practice paper

Maximum Marks: 40Suggested time: 60 minutes

Instructions: Answer all 20 questions. Marks are shown in brackets. Show calculation steps and units. Original practice questions, not an official examination paper.

Section A · 1-mark questions — 8 × 1 = 8 marks

Define centre of mass.[1]
Torque magnitude?[1]
SI unit of moment of inertia?[1]
Rotational kinetic energy?[1]
Condition for angular momentum conservation?[1]
Rolling relation?[1]
Static rigid-body equilibrium?[1]
Parallel-axis theorem?[1]

Section B · 2-mark questions — 6 × 2 = 12 marks

2 and 3 kg at x=0 and 5 m: x_cm?[2]
4 N perpendicular at .5 m: torque?[2]
I=3 kg m², ω=4: rotational energy?[2]
Radius .4 m wheel at 8 m/s: ω?[2]
Torque 12 N m and I=4: α?[2]
No external force: total momentum?[2]

Section C · 3-mark questions — 4 × 3 = 12 marks

2 kg at x=0 and 6 kg at x=4: x_cm?[3]
.25 m spanner, 40 N at 30°: torque?[3]
Solid disc M=4 kg, R=.5 m: I and KE at ω=10?[3]
ω rises 2 to 10 rad/s in 4 s: α and θ?[3]

Section D · 4-mark questions — 2 × 4 = 8 marks

2 kg at x=0 and 3 kg at x=5 m, external force 10 N: x_cm and acceleration?[4]
Skater I changes 4 to 1.6 kg m² from ω=3: final ω and KE change?[4]

End of paper — review signs, units and working.

Open marking scheme and model answers

Attempt the paper before opening the key. Multi-mark answers show expected principles and results; award partial credit for valid intermediate steps.

Q1 · 1 mark
Mass-weighted mean position.
Suggested allocation by section: 1-mark questions earn one mark for the correct fact, formula or unit; 2-mark questions normally award one mark for the principle/formula and one for the explanation or result; 3-mark questions award credit for the relation, working/reasoning and result with unit; 4-mark questions award credit for the principle, equation, working and final answer/interpretation. Accept equivalent correct methods.

Q2 · 1 mark
rF sinθ.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q3 · 1 mark
kg m².
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q4 · 1 mark
½Iω².
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q5 · 1 mark
Net external torque is zero.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q6 · 1 mark
v=rω.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q7 · 1 mark
ΣF=0 and Στ=0.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q8 · 1 mark
I=I_cm+Md².
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q9 · 2 marks
3 m.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q10 · 2 marks
2 N m.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q11 · 2 marks
24 J.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q12 · 2 marks
20 rad/s.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q13 · 2 marks
3 rad/s².
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q14 · 2 marks
Constant.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q15 · 3 marks
3 m.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q16 · 3 marks
5 N m.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q17 · 3 marks
I=.5 kg m²; K=25 J.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q18 · 3 marks
2 rad/s²; 24 rad.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q19 · 4 marks
3 m; 2 m/s².
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.

Q20 · 4 marks
ω=7.5 rad/s; K increases 18 to 45 J because skater does work.
Suggested credit: award marks for the correct principle, working and result as applicable; accept equivalent correct methods.