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Define angular displacement ($\theta$).
The angle through which a point or line has been rotated in a specified direction.
Define angular velocity ($\omega$).
The rate of change of angular displacement with respect to time.
Define angular acceleration ($\alpha$).
The rate of change of angular velocity with respect to time.
Define arc length ($s$).
The distance along a curved path.
Define tangential acceleration ($a_t$).
The component of acceleration of a point on a rotating object that is tangent to the circle of motion.
What is a 'rigid rotating system'?
A system that maintains its shape and size during rotation, where all points share the same angular velocity and angular acceleration.
What is the difference between linear and angular displacement?
Linear displacement: distance traveled along a straight line. Angular displacement: angle through which an object has rotated.
What is the difference between linear and angular velocity?
Linear velocity: rate of change of linear displacement. Angular velocity: rate of change of angular displacement.
What is the difference between linear and tangential acceleration?
Linear acceleration: rate of change of velocity in a straight line. Tangential acceleration: rate of change of tangential velocity of a rotating object.
Compare angular velocity at different points in a rigid rotating system.
All points in a rigid rotating system share the same angular velocity, regardless of their distance from the axis of rotation.
Compare tangential velocity at different points in a rigid rotating system.
Points further from the axis of rotation in a rigid rotating system have greater tangential velocity.
What is the effect of applying a constant tangential force to the edge of a disk?
It causes the disk to experience angular acceleration and thus rotate with increasing angular velocity.
What is the effect of increasing the radius on the linear velocity of a point on a rotating object, given a constant angular velocity?
The linear velocity of the point increases.
What is the effect of a non-zero angular acceleration?
The angular velocity of the object changes over time.
What is the effect of applying a torque to an object?
It causes the object to experience angular acceleration.
What happens to the tangential acceleration if the angular acceleration increases?
The tangential acceleration increases proportionally, given a constant radius.