When a rigid body rotates about a fixed axis, we need to consider which physical quantities are conserved under such motion. Conservation laws are fundamental in physics and depend on the external forces and torques acting on the system.
B) Angular momentum
Angular momentum (\(L\)) for a rigid body rotating about a fixed axis is given by \(L = I\omega\), where \(I\) is the moment of inertia and \(\omega\) is the angular velocity. If no external torque acts on the body, its angular momentum remains constant. Even if external forces act, if their net torque about the fixed axis is zero, angular momentum is conserved. For a rigid body rotating about a fixed axis, the moment of inertia \(I\) is constant. If the angular momentum is conserved, then the angular velocity \(\omega\) must also be constant, meaning the rotation is uniform.
The question asks for the standard unit of measurement for angular displacement. We need to recall the definitions of angular displacement and its common units.
Correct Option: A) radians is the SI unit for angular displacement and is the preferred unit in scientific and engineering calculations involving rotational motion.
According to Newton's second law for rotational motion, the torque acting on an object is equal to the rate of change of its
This question tests understanding of Newton's second law as applied to rotational motion. The rotational analogue of force is torque, and the rotational analogue of linear momentum is angular momentum. Just as force is the rate of change of linear momentum, torque is the rate of change of angular momentum.
Correct Option: B) angular momentum. According to Newton's second law for rotational motion, the torque acting on an object is equal to the rate of change of its angular momentum. This is a fundamental principle in rotational dynamics.
The moment of inertia is a measure of an object's resistance to angular acceleration. It is the rotational analogue of mass in linear motion. We need to understand the factors that determine this property.
Correct Option: A) shape and mass distribution. This option correctly identifies the two primary factors that determine the moment of inertia: the overall shape (which dictates how mass is distributed) and the mass distribution itself (how mass elements are positioned relative to the axis of rotation).
This question tests the understanding of rotational dynamics, specifically the relationship between torque and angular momentum. The key concept is the conservation of angular momentum when the net external torque is zero.
To determine the correct statement about the conservation of angular momentum, we need to recall the fundamental principles of rotational dynamics, specifically Newton's second law for rotation.
Correct Option: A) Angular momentum is conserved only if no external torque acts on the system. This statement directly follows from Newton's second law for rotation, which states that the net external torque is equal to the rate of change of angular momentum. If the net external torque is zero, then the angular momentum remains constant (is conserved).