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Which of the following quantities is zero if the torque on a particle is zero?

a) Angular momentum of the particle
b) Angular speed of the particle
c) Change in kinetic energy of the particle
d) Rate of change of angular momentum

Sagot :

Rochirionidn

Answer:

d) Rate of change of angular momentum

Explanation:

To determine which quantity is zero if the torque on a particle is zero, we need to understand the relationship between torque and these physical quantities.

Understanding Torque and Angular Momentum:

Torque (τ) is related to the rate of change of angular momentum (L) by the equation:

[tex]\tau = \dfrac{dL}{dt}[/tex]

If the torque on a particle is zero (τ = 0), then the rate of change of angular momentum is also zero:

[tex]\dfrac{dL}{dt}=0[/tex]

This means that the angular momentum 'L' of the particle is constant over time.

Analyzing the Options:

  • (a) Angular momentum of the particle: If the torque is zero, the angular momentum is constant, but not necessarily zero.

  • (b) Angular speed of the particle: The angular speed could remain constant or change depending on other forces acting on the particle, so this is not necessarily zero.

  • (c) Change in kinetic energy of the particle: Kinetic energy change is related to work done, which depends on forces, not directly on torque.

  • (d) Rate of change of angular momentum: As derived above, if torque is zero, the rate of change of angular momentum is zero.

The correct answer is (d) Rate of change of angular momentum. If the torque on a particle is zero, the rate of change of angular momentum must also be zero.

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