NEET System of Particles and Rotational Motion — Set 9

Question 1

A particle rotates about a fixed axis at a radius of $ 0.3 \, \text{m} $ with a linear speed of $ 6 \, \text{m/s} $. What is its angular velocity?

Accepted Answer

$ v = \omega r $. $ v = 6 \, \text{m/s} $, $ r = 0.3 \, \text{m} $. $ \omega = \frac{v}{r} = \frac{6}{0.3} = 20 \, \text{rad/s} $.

Question 2

A solid cylinder of mass $ 4 \, \text{kg} $ and radius $ 0.3 \, \text{m} $ rotates about its axis at $ 6 \, \text{rad/s} $. What is its rotational kinetic energy?

Accepted Answer

$ I = \frac{1}{2} M R^2 = \frac{1}{2} \times 4 \times (0.3)^2 = 0.18 \, \text{kg m}^2 $. $ K = \frac{1}{2} I \omega^2 = \frac{1}{2} \times 0.18 \times (6)^2 = 0.09 \times 36 = 3.24 \, \text{J} $.

Question 3

A torque of $ 20 \, \text{Nm} $ acts on a wheel with moment of inertia $ 10 \, \text{kg m}^2 $ starting from rest. What is its angular speed after $ 4 \, \text{s} $?

Accepted Answer

$ \alpha = \frac{\tau}{I} = \frac{20}{10} = 2 \, \text{rad/s}^2 $. $ \omega = \omega_0 + \alpha t = 0 + 2 \times 4 = 8 \, \text{rad/s} $.

NEET Physics: System of Particles and Rotational Motion — Practice Set 9

Q1. A particle rotates about a fixed axis at a radius of \( 0.3 \, \text{m} \) with a linear speed of \( 6 \, \text{m/s} \). What is its angular velocity?

Q2. A solid cylinder of mass \( 4 \, \text{kg} \) and radius \( 0.3 \, \text{m} \) rotates about its axis at \( 6 \, \text{rad/s} \). What is its rotational kinetic energy?

Q3. A torque of \( 20 \, \text{Nm} \) acts on a wheel with moment of inertia \( 10 \, \text{kg m}^2 \) starting from rest. What is its angular speed after \( 4 \, \text{s} \)?

Q4. A thin ring of mass \( 2 \, \text{kg} \) and radius \( 0.7 \, \text{m} \) rolls without slipping with a linear speed of \( 3.5 \, \text{m/s} \). What is its angular velocity?

Q5. A thin ring of mass \( 2 \, \text{kg} \) and radius \( 0.4 \, \text{m} \) has a kinetic energy of \( 8 \, \text{J} \). What is its angular speed?

Q6. A \( 1 \, \text{kg} \) mass rotates in a circle of radius \( 0.8 \, \text{m} \) with a speed of \( 5 \, \text{m/s} \). What is its angular momentum about the center?

Q7. What happens to the rotational kinetic energy if the angular velocity of a body is halved?

Q8. A solid cylinder of mass \( 2 \, \text{kg} \) and radius \( 0.1 \, \text{m} \) rotates about its axis at \( 20 \, \text{rad/s} \). What is its rotational kinetic energy?

Q9. A torque of \( 18 \, \text{Nm} \) is applied to a wheel with moment of inertia \( 9 \, \text{kg m}^2 \). What is its angular acceleration?

Q10. A solid cylinder of mass \( 5 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) has an angular momentum of \( 12.5 \, \text{kg m}^2/\text{s} \). What is its angular velocity?