Vidaara.orgClass 11 · Physics
CodeVID-P11-06-TOR-01
Torque, Moment of Inertia & Angular Momentum — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The SI unit of torque is the:
- A.newton
- B.joule
- C.newton metre
- D.watt
2.
The moment of inertia of a solid sphere about a diameter is:
- A.$MR^2$
- B.$\frac{1}{2}MR^2$
- C.$\frac{2}{5}MR^2$
- D.$\frac{2}{3}MR^2$
3.
Angular momentum equals:
- A.$I\alpha$
- B.$I\omega$
- C.$\tfrac{1}{2}I\omega^2$
- D.$\tau r$
4.
Radius of gyration $k$ equals:
- A.$I/M$
- B.$\sqrt{I/M}$
- C.$MI$
- D.$M/I$
5.
Moment of inertia depends on:
- A.mass only
- B.axis position only
- C.mass and its distribution about the axis
- D.speed only
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
A 40 N force acts perpendicular to a 0.3 m spanner. Find the torque.
7.
A disc with $I=0.4\ \text{kg m}^2$ spins at $5\ \text{rad/s}$. Find $L$.
8.
Define radius of gyration.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
A solid cylinder of mass 6 kg and radius 0.2 m rotates about its axis. Find $I$ and $k$.
10.
A wheel of $I=2\ \text{kg m}^2$ spinning at $6\ \text{rad/s}$ is connected to a stationary wheel of $I=4\ \text{kg m}^2$. Find the common angular speed.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Define torque and angular momentum. State the law of conservation of angular momentum and explain how a diver curls up to complete more somersaults.
Answer Key
Section A — Multiple Choice Questions
- (C) newton metre
- (C) $\frac{2}{5}MR^2$
- (B) $I\omega$
- (B) $\sqrt{I/M}$
- (C) mass and its distribution about the axis
Section B — Short Answer (2 marks)
- $\tau=12\ \text{N m}$.
- $L=2\ \text{kg m}^2\text{/s}$.
- The distance $k$ from the axis at which the whole mass could be placed to give the same $I$: $I=Mk^2$.
Section C — Short Answer (3 marks)
- $I=0.12\ \text{kg m}^2$; $k\approx0.141\ \text{m}$.
- By conservation of $L$: $\omega=\frac{2\times6}{6}=2\ \text{rad/s}$.
Section D — Long Answer (5 marks)
- $\vec{\tau}=\vec{r}\times\vec{F}$, $L=I\omega$; with zero external torque $L$ is constant, so curling up reduces $I$ and increases $\omega$, letting the diver spin faster.
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