The angular momentum of a system remains constant when:
A. the total kinetic energy is constant
B. when no net external force acts on the system
C. when the linear momentum and the energy are constant
D. when no torque acts on the system
E. all the time since it is a conserved quantity
The correct answer and explanation is:
The correct answer is D. when no torque acts on the system.
Explanation:
Angular momentum is a measure of the rotational motion of an object or system. The angular momentum of a system is defined as the cross product of the position vector and the linear momentum of the particles in the system. Mathematically, the angular momentum LL is given by: L=r×pL = r \times p
where rr is the position vector and pp is the linear momentum of the object.
In classical mechanics, the angular momentum of a system remains constant if the net external torque acting on the system is zero. This principle is derived from the law of conservation of angular momentum. According to this law, if no external torque is applied to a system, the angular momentum will remain unchanged.
Torque is defined as the rate of change of angular momentum with respect to time: τ=dLdt\mathbf{\tau} = \frac{d\mathbf{L}}{dt}
Therefore, if the net external torque τ\mathbf{\tau} is zero, then: dLdt=0\frac{d\mathbf{L}}{dt} = 0
This implies that the angular momentum L\mathbf{L} is conserved and does not change over time.
It is important to note that while angular momentum is conserved in the absence of external torque, it is not necessarily related to constant kinetic energy or linear momentum. The system can have varying kinetic energy or linear momentum while still conserving angular momentum, provided that no external torque is acting.
Thus, angular momentum conservation is directly tied to the absence of external torques rather than other factors such as energy or linear momentum conservation.