Question

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle \(\theta\) .The frictional force 

• A. converts translational energy to rotational energy
• B. dissipates energy as heat
• C. decreases the rotational motion
• D. decreases the rotational and translational motion

Answer 1

The Correct Option is A

To solve the given problem, we need to understand the physics behind the rolling motion of a drum down an inclined plane.

When a drum or cylinder rolls down an inclined plane without slipping, both translational motion (linear) and rotational motion (angular) occur simultaneously. The frictional force plays a crucial role in this motion.

1. Translational and Rotational Motion:
   • The drum has a translational kinetic energy due to its linear motion down the incline.
   • It also has rotational kinetic energy as it spins about its axis.
2. Role of Friction:
   • The frictional force ensures that the drum rolls without slipping. This type of friction is static friction.
   • Instead of converting mechanical energy into heat (as dynamic friction would), this static friction facilitates the conversion of translational kinetic energy into rotational kinetic energy.
3. Explanation of Options:
   • Converts translational energy to rotational energy: This is the correct option. The static friction responsible for rolling without slipping transforms the linear movement energy into rotational energy, allowing the drum to rotate as it translates down the incline.
   • Dissipates energy as heat: Incorrect, as static friction does not lead to energy dissipation through heat.
   • Decreases the rotational motion: Incorrect, as static friction supports rotational motion.
   • Decreases the rotational and translational motion: Incorrect, since static friction does not reduce but maintains or supports motion integrity by preventing slipping.

In conclusion, the correct answer is that the frictional force converts translational energy to rotational energy.