NEET System of Particles and Rotational Motion — Set 10

Question 1

A solid cylinder with moment of inertia $ 2 \, \text{kg m}^2 $ is acted upon by a torque of $ 10 \, \text{Nm} $. What is its angular acceleration?

Accepted Answer

$ \tau = I \alpha $. $ \tau = 10 \, \text{Nm} $, $ I = 2 \, \text{kg m}^2 $. $ \alpha = \frac{\tau}{I} = \frac{10}{2} = 5 \, \text{rad/s}^2 $.

Question 2

Which property of a rigid body remains constant during rotation about a fixed axis?

Accepted Answer

For a rigid body rotating about a fixed axis, all particles have the same angular velocity, which is a property of the body’s rotation and remains constant across all points.

Question 3

A torque of $ 15 \, \text{Nm} $ acts on a wheel with moment of inertia $ 5 \, \text{kg m}^2 $ starting from rest. What is its angular speed after $ 3 \, \text{s} $?

Accepted Answer

$ \alpha = \frac{\tau}{I} = \frac{15}{5} = 3 \, \text{rad/s}^2 $. $ \omega = \omega_0 + \alpha t = 0 + 3 \times 3 = 9 \, \text{rad/s} $.

NEET Physics: System of Particles and Rotational Motion — Practice Set 10

Q1. A solid cylinder with moment of inertia \( 2 \, \text{kg m}^2 \) is acted upon by a torque of \( 10 \, \text{Nm} \). What is its angular acceleration?

Q2. Which property of a rigid body remains constant during rotation about a fixed axis?

Q3. A torque of \( 15 \, \text{Nm} \) acts on a wheel with moment of inertia \( 5 \, \text{kg m}^2 \) starting from rest. What is its angular speed after \( 3 \, \text{s} \)?

Q4. A hollow cylinder of mass \( 2 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has an angular momentum of \( 10 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

Q5. A solid sphere of mass \( 1 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has a kinetic energy of \( 5 \, \text{J} \). What is its angular speed?

Q6. A \( 1 \, \text{kg} \) mass rotates in a circle of radius \( 0.9 \, \text{m} \) with a speed of \( 6 \, \text{m/s} \). What is its angular momentum about the center?

Q7. Which factor does not affect the moment of inertia of a rigid body?

Q8. A hollow cylinder of mass \( 2 \, \text{kg} \) and radius \( 0.8 \, \text{m} \) has an angular momentum of \( 16 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

Q9. What is the rotational analogue of mass in Newton’s second law?

Q10. A thin ring of mass \( 5 \, \text{kg} \) and radius \( 0.2 \, \text{m} \) rotates at \( 10 \, \text{rad/s} \). What is its angular momentum?