NEET System of Particles and Rotational Motion — Set 17

Question 1

A particle rotates about a fixed axis at a radius of $ 0.6 \, \text{m} $ with a linear speed of $ 3 \, \text{m/s} $. What is its angular velocity?

Accepted Answer

$ v = \omega r $. $ v = 3 \, \text{m/s} $, $ r = 0.6 \, \text{m} $. $ \omega = \frac{v}{r} = \frac{3}{0.6} = 5 \, \text{rad/s} $.

Question 2

A $ 5 \, \text{kg} $ block slides down an inclined plane with a constant velocity of $ 2 \, \text{m/s} $. What is the velocity of the center of mass of the block?

Accepted Answer

For a single body in pure translational motion, the velocity of the center of mass is the same as the velocity of the body. Given: $ v = 2 \, \text{m/s} $. Thus, $ \mathbf{V} = 2 \, \text{m/s} $ (direction along the incline).

Question 3

A torque of $ 14 \, \text{Nm} $ acts on a wheel with moment of inertia $ 7 \, \text{kg m}^2 $ starting from rest. What is its angular speed after $ 5 \, \text{s} $?

Accepted Answer

$ \alpha = \frac{\tau}{I} = \frac{14}{7} = 2 \, \text{rad/s}^2 $. $ \omega = \omega_0 + \alpha t = 0 + 2 \times 5 = 10 \, \text{rad/s} $.

NEET Physics: System of Particles and Rotational Motion — Practice Set 17

Q1. A particle rotates about a fixed axis at a radius of \( 0.6 \, \text{m} \) with a linear speed of \( 3 \, \text{m/s} \). What is its angular velocity?

Q2. A \( 5 \, \text{kg} \) block slides down an inclined plane with a constant velocity of \( 2 \, \text{m/s} \). What is the velocity of the center of mass of the block?

Q3. A torque of \( 14 \, \text{Nm} \) acts on a wheel with moment of inertia \( 7 \, \text{kg m}^2 \) starting from rest. What is its angular speed after \( 5 \, \text{s} \)?

Q4. Which physical quantity is defined as \( \mathbf{r} \times \mathbf{p} \) for a particle?

Q5. What is the condition for a rigid body to have zero angular acceleration?

Q6. Why can a rigid body not deform under the influence of forces in theoretical mechanics?

Q7. Three particles of masses \( 3 \, \text{kg} \), \( 6 \, \text{kg} \), and \( 9 \, \text{kg} \) are located at \( (0, 1) \), \( (2, 2) \), and \( (4, 0) \) respectively. What is the x-coordinate of their center of mass?

Q8. A torque of \( 15 \, \text{Nm} \) is applied to a wheel with moment of inertia \( 3 \, \text{kg m}^2 \). What is its angular acceleration?

Q9. A solid sphere of mass \( 3 \, \text{kg} \) and radius \( 0.4 \, \text{m} \) rotates about its center at \( 5 \, \text{rad/s} \). What is its rotational kinetic energy?

Q10. Three particles of masses \( 1 \, \text{kg} \), \( 5 \, \text{kg} \), and \( 10 \, \text{kg} \) are at \( (0, 2) \), \( (3, 0) \), and \( (4, 6) \) respectively. What is the x-coordinate of their center of mass?