Physics · Basic concepts of rotational motion, moment of a force, torque, angular momentum, conservation of angular momentum and its applications
A sphere rolls without sliding on a rough inclined plane (only mg and contact fo
A sphere rolls without sliding on a rough inclined plane (only mg and contact forces are acting on the body). The angular momentum, of the body:
- A. about centre is conserved
- B. is conserved about the point of contact
- C. is conserved about a point whose distance from the inclined plane is greater than the radius of the sphere
- D. is not conserved about any point
Step-by-step solution
For a sphere rolling without slipping on a rough inclined plane, the net external torque about any fixed point with y-coordinate (distance from plane) equal to (7/5)R is zero, where R is the radius. This follows from setting the total torque (sum of torques from gravity, normal, and friction) to zero, leading to y_Q = (7/5)R > R. Hence, angular momentum is conserved about such a point.
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