Rotational motion is the motion of a body around a fixed axis or point.
Define angular displacement.
Angular displacement is the angle through which a point, line, or body is rotated in a specified direction and about a specified axis.
What is angular velocity?
Angular velocity is the rate of change of angular displacement with time. It is measured in radians per second.
Explain the concept of moment of inertia.
Moment of inertia is a measure of an object's resistance to changes in its rotation and depends on the mass distribution relative to the axis of rotation.
What is the formula for calculating torque?
Torque is calculated using the formula τ = r × F × sin(θ), where τ is torque, r is the lever arm, F is the force applied, and θ is the angle between the force and lever arm.
How does centripetal force relate to rotational motion?
Centripetal force is needed to keep an object moving in a circular path and acts perpendicular to the motion towards the center of rotation.
What is the principle of conservation of angular momentum?
The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum remains constant.
Define angular acceleration.
Angular acceleration is the rate of change of angular velocity over time, typically measured in radians per second squared.
How is kinetic energy computed in rotational motion?
Rotational kinetic energy is given by the formula KE_rotational = (1/2) I ω², where I is the moment of inertia and ω is the angular velocity.
What role does the radius of gyration play in rotational motion?
The radius of gyration is a measure of the distribution of an object's mass around its axis of rotation.
Describe the role of gyroscopic effects in stabilizing motion.
Gyroscopic effects help stabilize moving objects by utilizing angular momentum, which resists changes in orientation.
What is precession and how does it occur?
Precession is the slow change in the orientation of a spinning object's rotational axis due to an external force or torque.
How does rolling motion relate to rotational motion?
Rolling motion is a combination of translational and rotational motion, where an object rotates as it moves along a surface.
Explain the concept of rotational equilibrium.
Rotational equilibrium occurs when the net torque acting on an object is zero, resulting in no change in its rotational motion.
What is the significance of the angular momentum vector?
The angular momentum vector represents the magnitude and direction of angular momentum, calculated by L = Iω.