Question

When the net torque on an object is zero, its angular momentum stays ________?

1) constant
2) increased
3) decreased
4) not affected

Answer 1

When the net torque on an object is zero, its angular momentum stays **constant**. Thus the correct option is (1).

Step-by-step explanation:

Angular momentum L is defined as the product of moment of inertia I and angular velocity
`(\(\omega\)),` represented by the equation
`\(L = I \cdot \omega\).`The net torque
`(\(\tau\))` acting on an object is related to its angular momentum by the equation
`\(\tau = I \cdot \alpha\),` where
`\(\alpha\)` is the angular acceleration. When the net torque is zero
`(\(\tau = 0\)),` this implies that the angular acceleration is also zero
`(\(\alpha = 0\)).`Thus the correct option is (1).

In the absence of angular acceleration, the angular velocity
`(\(\omega\))`remains constant. Therefore, using the angular momentum equation
`(\(L = I \cdot \omega\)),` if
`(\alpha\)` is zero, then L must be constant. This is consistent with the law of conservation of angular momentum, stating that the total angular momentum of an isolated system remains constant if no external torque is applied.

To further illustrate, consider a spinning ice skater pulling in their arms. As they do so, their moment of inertia decreases, leading to an increase in angular velocity to conserve angular momentum. Conversely, when no external torque acts on the system, as in the case when the net torque is zero, there is no change in angular momentum, and the angular velocity remains constant. This fundamental principle holds true for a wide range of rotational motion scenarios, emphasizing the significance of angular momentum conservation.

Answer 2

1) constant

Step-by-step explanation:

To address the question of what happens to an object's angular momentum when the net torque is zero, we'll apply the principles of rotational dynamics.

When the net torque on an object is zero, its angular momentum stays constant. This statement is a consequence of the conservation of angular momentum, which is a fundamental principle in physics. The law of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. This is analogous to the principle of conservation of linear momentum, where the linear momentum of a system remains constant if no external force acts on it.

Options (2) and (3) would imply a change in angular momentum, which would require a net external torque, contradicting the condition stated in the question. Option (4) is a bit ambiguous but could be interpreted as meaning the angular momentum doesn't change, which aligns with option (1), the correct answer.