System of Particles and Rotational Motion quiz

The centre of mass of a uniform rod lies at its:

The motion of the centre of mass of a system is affected by:

The SI unit of torque is:

The SI unit of angular momentum is:

The moment of inertia of a body depends on:

Torque is equal to the rate of change of:

A skater pulls her arms in while spinning. Her angular speed:

In rotational motion, the quantity analogous to mass is:

The moment of inertia of a thin ring of mass M and radius R about its axis is:

Work done by a constant torque tau turning a body through angle theta is:

Distinguish between translational and rotational motion of a rigid body. (2 marks)

What is a rigid body? (2 marks)

Explain why a shell exploding in mid-air does not change the path of its centre of mass. (2 marks)

State the conditions for the mechanical equilibrium of a rigid body. (2 marks)

Define the moment of inertia of a body. (2 marks)

Why is it easier to open a tight nut with a long spanner? (2 marks)

Write the rotational analogues of F = ma and p = mv. (2 marks)

Explain why a diver tucks in her body during a somersault. (2 marks)

What is a couple? Give an example. (2 marks)

Find the angular momentum of a 0.2 kg particle moving at 5 m/s in a circle of radius 2 m. (2 marks)

A girl of 30 kg sits 2 m from the pivot of a seesaw. Where must a boy of 40 kg sit on the other side to balance it? (3 marks)

A disc of moment of inertia 0.5 kg m^2 rotates at 20 rad/s. Find its rotational kinetic energy. (3 marks)

A wheel turning at 10 rad/s stops uniformly in 5 s. Find its angular deceleration and the angle turned. (3 marks)

A motor delivers a torque of 50 N m to a wheel turning at 20 rad/s. Find the power delivered. (3 marks)

A skater spinning at 2 rev/s has moment of inertia 4 kg m^2. She reduces it to 2 kg m^2. Find her new angular speed. (3 marks)

Read the passage and answer the questions. A ceiling fan starts from rest and reaches 10 rad/s in 5 s with uniform angular acceleration. (i) Find its angular acceleration. (ii) Find the angle turned in 5 s. (iii) If its moment of inertia is 0.2 kg m^2, find the torque applied. (5 marks)

Read the passage and answer the questions. A shell is fired along a parabolic path and explodes in mid-air into two fragments. (i) Do the internal forces of the explosion change the path of the centre of mass? (ii) Along what path does the centre of mass continue? (iii) Which quantity of the system is conserved during the explosion? (5 marks)

Read the passage and answer the questions. A mechanic loosens a nut with a spanner 0.25 m long, applying 40 N at right angles. (i) Find the torque applied. (ii) What force is needed with a 0.5 m spanner? (iii) Why do mechanics sometimes add a pipe to the spanner handle? (5 marks)

Read the passage and answer the questions. An ice skater spins with arms outstretched at 1 rev/s. Her moment of inertia is 6 kg m^2. She pulls in her arms, reducing it to 2 kg m^2. (i) Which quantity is conserved? (ii) Find her new angular speed. (iii) Does her rotational kinetic energy change? Explain. (5 marks)

Read the passage and answer the questions. Two children balance a seesaw. A child of 25 kg sits 2 m from the pivot. (i) State the condition for balance. (ii) Where should a 50 kg adult sit to balance the child? (iii) What is the net torque on the balanced seesaw? (5 marks)

Derive the expression for the centre of mass of a system of n particles and explain the motion of the centre of mass. (6 marks)

Define the vector product of two vectors and state its properties. Use it to define torque and angular momentum. (6 marks)

Show that the torque on a particle equals the rate of change of its angular momentum, and hence state the conservation of angular momentum. (6 marks)

Explain the equilibrium of a rigid body. Explain the principle of moments using a lever. (6 marks)

Compare translational and rotational motion about a fixed axis, writing the analogous quantities and equations of motion. (6 marks)