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Compare linear displacement ($Delta x$) and angular displacement ($Delta heta$).
Linear displacement: Change in position along a straight line. | Angular displacement: Change in angular position around an axis.
Compare linear velocity ($v$) and angular velocity ($omega$).
Linear velocity: Rate of change of linear displacement. | Angular velocity: Rate of change of angular displacement.
Compare linear acceleration ($a$) and angular acceleration ($alpha$).
Linear acceleration: Rate of change of linear velocity. | Angular acceleration: Rate of change of angular velocity.
What is the difference between clockwise and counterclockwise rotation in terms of sign convention?
Clockwise rotation: Typically assigned a negative value. | Counterclockwise rotation: Typically assigned a positive value.
When can a rotating system be treated as a single object?
When the system's rotation is well described by its center of mass motion.
Compare torque and force.
Force causes linear acceleration; torque causes angular acceleration. Torque is the rotational analog of force.
Compare moment of inertia and mass.
Mass is resistance to linear acceleration; moment of inertia is resistance to angular acceleration. Moment of inertia depends on mass distribution.
Compare angular momentum and linear momentum.
Linear momentum is mass times velocity; angular momentum is moment of inertia times angular velocity. Both are conserved in closed systems.
Compare angular velocity and linear velocity.
Angular velocity (ω) is the rate of change of angular displacement; linear velocity (v) is the rate of change of linear displacement. v = rω
Compare angular acceleration and linear acceleration.
Angular acceleration (α) is the rate of change of angular velocity; linear acceleration (a) is the rate of change of linear velocity. a = rα
Define torque.
Torque is the rotational equivalent of force, causing objects to rotate.
Define angular displacement.
The change in the angle of a rotating object, measured in radians.
Define angular velocity.
The rate of change of angular displacement, measured in radians per second.
Define angular acceleration.
The rate of change of angular velocity, measured in radians per second squared.
Define moment of inertia.
The rotational equivalent of mass, measuring an object's resistance to changes in rotational motion.
Define angular momentum.
The rotational equivalent of linear momentum, measuring an object's tendency to keep rotating.