Question

When a particle is rotating with constant angular momentum, then

• A. torque acting on it is constant
• B. force acting on it is constant
• C. linear momentum is constant
• D. torque acting on it is zero
• E. linear velocity is constant

Hint:

Constant angular momentum $\Rightarrow$ no external torque.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question relates to the fundamental principle of rotational dynamics, which connects torque (\(\vec{\tau}\)) and angular momentum (\(\vec{L}\)). This relationship is the rotational analogue of Newton's Second Law for linear motion (\(\vec{F} = d\vec{p}/dt\)).
Step 2: Key Formula or Approach:
The net external torque acting on a particle or a system is equal to the rate of change of its angular momentum. \[ \vec{\tau} = \frac{d\vec{L}}{dt} \] Step 3: Detailed Explanation:
We are given that the particle is rotating with constant angular momentum. "Constant" means that the angular momentum vector \(\vec{L}\) does not change with time, neither in magnitude nor in direction. If \(\vec{L}\) is constant, its time derivative must be zero: \[ \frac{d\vec{L}}{dt} = 0 \] From the formula relating torque and angular momentum, we have: \[ \vec{\tau} = \frac{d\vec{L}}{dt} = 0 \] This means that the net external torque acting on the particle must be zero. Let's analyze the other options:
(A) "torque acting on it is constant" is not necessarily true. It must be a specific constant: zero.
(B) "force acting on it is constant" is incorrect. For rotation (even at constant speed), there must be a centripetal force, which constantly changes direction.
(C) "linear momentum is constant" is incorrect. Since the particle is rotating, its velocity vector \(\vec{v}\) is continuously changing direction, so its linear momentum \(\vec{p} = m\vec{v}\) is also not constant.
(E) "linear velocity is constant" is incorrect for the same reason as (C); the direction of velocity changes during rotation.
Step 4: Final Answer:
When angular momentum is constant, the net torque acting on the particle is zero.