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 (ฯ) is the rate of change of angular displacement; linear velocity (v) is the rate of change of linear displacement. v = rฯ
Compare angular acceleration and linear acceleration.
Angular acceleration (ฮฑ) is the rate of change of angular velocity; linear acceleration (a) is the rate of change of linear velocity. a = rฮฑ
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.
What is the effect of applying a torque on an object?
It causes the object to undergo angular acceleration.
What happens when the net torque on an object is zero?
The object is in rotational equilibrium; its angular velocity remains constant.
What happens when a figure skater pulls their arms inward?
Their moment of inertia decreases, and their angular speed increases to conserve angular momentum.
What is the effect of increasing the distance from the axis of rotation when applying a force?
It increases the torque, making it easier to cause rotational motion.
What happens if no external torque acts on a rotating system?
The total angular momentum of the system remains constant.
What happens when the moment of inertia increases?
The object becomes more resistant to changes in rotational motion, requiring more torque to achieve the same angular acceleration.
