Class 12th Physics Question: Rolling Motion and Friction

This blog discusses a key topic in Class 12th Physics Board exams: rolling motion and friction. We’ll solve a conceptual question often asked in exams to enhance your understanding.

Class 12 physics board question


Modified Question

A horizontal force F is applied at the center of mass of a cylindrical object of mass M and radius R, perpendicular to its axis. The coefficient of friction between the object and the ground is μ. The center of mass of the object has an acceleration A. The acceleration due to gravity is g. Given that the object rolls without slipping, analyze the following statements:

  • The force of friction acts in the opposite direction of motion.
  • The angular acceleration of the cylinder is proportional to the net torque acting on it.
  • The condition for rolling without slipping is A = μg.
  • The force F is equal to the sum of the frictional force and the net accelerating force.

Solution

To solve this question, we apply the principles of rolling motion:

  1. Force Analysis: The total force on the object is the applied force F minus the frictional force f. The net force causes linear acceleration:

    F - f = MA
  2. Torque Analysis: The torque due to friction provides angular acceleration:

    fR = Iα, where I is the moment of inertia and α is the angular acceleration.
  3. Rolling Condition: For rolling without slipping, the linear and angular accelerations are related by:

    A = αR.

Step-by-Step Calculations

Substituting the moment of inertia of a solid cylinder (I = 0.5MR²) and the rolling condition into the equations above, we derive:

F = (3/2)MA and f = (1/3)F.

Thus, the correct statements are:

  • The force of friction opposes motion.
  • The angular acceleration is proportional to torque.

Key Concepts for Class 12th Physics Board

  • Rolling Motion: Combines linear and rotational dynamics.
  • Frictional Force: Essential for rolling without slipping.
  • Moment of Inertia: Affects angular acceleration.

Conclusion

This problem integrates fundamental concepts of rolling motion and friction, often tested in the Class 12th Physics Board. Ensure you practice such questions thoroughly to excel in your exams!

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