"2024 Board Exam: Important Rotational Dynamics Questions for Class 12 Physics (Maharashtra Board)"

Important Questions for Chapter 1: Rotational Dynamics - Class 12 Physics

1. Conceptual Questions:

1. Define moment of inertia. How does the distribution of mass affect the moment of inertia of a rigid body?
2. What is radius of gyration? Explain its significance in rotational dynamics.
3. Explain the principle of conservation of angular momentum with examples.
4. Differentiate between torque and force.
5. What is rolling without slipping? Explain the condition for rolling without slipping in terms of linear and angular velocities.

2. Numerical Problems:

1. Calculate the moment of inertia of a solid cylinder about its central axis.
2. A thin circular ring of mass M and radius R is rotating about its diameter. Find its moment of inertia.
3. A disc of radius 0.5 m and mass 2 kg is rotating at 300 rpm. Calculate its angular momentum.
4. A solid sphere is rolling without slipping on a horizontal surface with a velocity of 10 m/s. Calculate the total kinetic energy of the sphere.
5. A rod of length 1 m and mass 2 kg is rotating about an axis perpendicular to the rod and passing through one of its ends. Find its moment of inertia.

3. Short Answer Questions:

1. State and prove the work-energy theorem for rotational motion.
2. Derive the relation between torque and angular momentum.
3. What is the parallel axis theorem? Derive the expression for it.
4. What is the perpendicular axis theorem? Where is it applicable? Explain with examples.
5. Derive an expression for the kinetic energy of a rotating body.

4. Application-Based Questions:

1. A gymnast increases her spin rate by pulling in her arms during a routine. Explain this phenomenon using the conservation of angular momentum.
2. Why is the moment of inertia of a ring about its diameter different from that about its central axis?
3. Discuss the real-life application of rolling without slipping. How does this concept apply to vehicles in motion?

5. Long Answer Questions:

1. Derive an expression for the moment of inertia of a solid sphere about its diameter.
2. Explain the concept of rolling motion and derive the relation between linear velocity and angular velocity for a body rolling without slipping.
3. Derive the equation for rotational kinetic energy of a rigid body and explain how it differs from translational kinetic energy.

6. Higher-Order Thinking Skill (HOTS) Questions:

1. A solid cylinder rolls down an inclined plane without slipping. Derive an expression for the velocity of the cylinder at the bottom of the incline using energy conservation.
2. How does angular momentum play a role in planetary motion?