NEET System of Particles and Rotational Motion — Set 18

Question 1

Why does a symmetric body rotating about its symmetry axis have angular momentum aligned with the axis?

Accepted Answer

Symmetry ensures perpendicular components of angular momentum cancel out, leaving $ \mathbf{L} = I \mathbf{\omega} $ aligned with the axis of rotation.

Question 2

A torque of $ 9 \, \text{Nm} $ is applied to a wheel with moment of inertia $ 3 \, \text{kg m}^2 $. What is its angular acceleration?

Accepted Answer

$ \tau = I \alpha $. $ \tau = 9 \, \text{Nm} $, $ I = 3 \, \text{kg m}^2 $. $ \alpha = \frac{\tau}{I} = \frac{9}{3} = 3 \, \text{rad/s}^2 $.

Question 3

A uniform disk of mass $ 4 \, \text{kg} $ and radius $ 0.5 \, \text{m} $ rotates at $ 8 \, \text{rad/s} $. What is its angular momentum about its axis?

Accepted Answer

$ L = I \omega $. For a disk: $ I = \frac{1}{2} M R^2 = \frac{1}{2} \times 4 \times (0.5)^2 = 0.5 \, \text{kg m}^2 $. $ L = 0.5 \times 8 = 4 \, \text{kg m}^2/\text{s} $.

NEET Physics: System of Particles and Rotational Motion — Practice Set 18

Q1. Why does a symmetric body rotating about its symmetry axis have angular momentum aligned with the axis?

Q2. A torque of \( 9 \, \text{Nm} \) is applied to a wheel with moment of inertia \( 3 \, \text{kg m}^2 \). What is its angular acceleration?

Q3. A uniform disk of mass \( 4 \, \text{kg} \) and radius \( 0.5 \, \text{m} \) rotates at \( 8 \, \text{rad/s} \). What is its angular momentum about its axis?

Q4. In rotational motion, what is the relationship between linear velocity and angular velocity for a particle?

Q5. A solid sphere of mass \( 3 \, \text{kg} \) and radius \( 0.4 \, \text{m} \) has an angular momentum of \( 12 \, \text{kg m}^2/\text{s} \). What is its angular velocity?

Q6. A uniform disk of mass \( 2 \, \text{kg} \) and radius \( 0.2 \, \text{m} \) rotates about its center with an angular speed of \( 10 \, \text{rad/s} \). What is its rotational kinetic energy?

Q7. For a body rotating about a fixed axis, what is true about particles on the axis?

Q8. Which of the following is true about the angular velocity of a rigid body rotating about a fixed axis?

Q9. A uniform rod of length \( 2 \, \text{m} \) and mass \( 4 \, \text{kg} \) lies along the x-axis with its left end at the origin. What is the position vector of its center of mass?

Q10. A solid sphere of mass \( 3 \, \text{kg} \) and radius \( 0.1 \, \text{m} \) rolls without slipping down an incline. If its linear speed is \( 5 \, \text{m/s} \), what is its angular velocity?