Rotational Kinematics

What is the core link between rotational and linear motion?

Linear motion is just rotation seen at a distance from the center. The farther out you are, the faster you move.

What is angular position (θ)?

How far something has rotated, like how much of a circle you’ve swept through (in radians).

What is angular displacement?

The change in rotation — imagine turning a steering wheel from left to right.

What is angular velocity (ω)?

How fast something spins — like how fast a fan blade rotates.

What is angular acceleration (α)?

How quickly the spinning speed is changing — like a fan speeding up.

What is the rotational version of position (x)?

Angular position (θ).

What is the rotational version of velocity (v)?

Angular velocity (ω).

What is the rotational version of acceleration (a)?

Angular acceleration (α).

What does v = rω actually mean physically?

Points farther from the center move faster, even though everything rotates together.

What does a_t = rα represent?

How fast the speed along the circle is changing.

What is centripetal acceleration?

Acceleration pointing toward the center that keeps something moving in a circle.

Why do you feel pulled outward on a ride?

Your body wants to move straight, but the force pulls you inward → feels like outward push.

What direction is centripetal acceleration always?

Toward the center of the circle.

What’s the rotational version of v = v_0 + at?

Same idea, but with angular quantities.

What’s the rotational version of displacement equation?

Same structure as linear, just replace x with θ.

What’s the biggest mistake students make here?

Mixing up linear and angular variables.

What am I doing when I calculate angular velocity?

Measuring how fast something spins around a center.

What am I doing when I use v = rω?

Converting spinning motion into straight-line speed.

What am I doing when I calculate centripetal acceleration?

Finding how hard something is being pulled inward to stay in a circle.

What am I doing when I use angular acceleration?

Tracking how quickly the spin speed is changing.

Why do all points on a rotating object have the same ω?

They complete each rotation together.

Why do outer points move faster?

They travel a larger circle in the same time.

What happens if radius increases?

Linear speed increases, angular speed stays the same.

Units of angular velocity?

rad/s.

Units of angular acceleration?

rad/s².

Units of θ?

radians.

How should I picture all of rotational motion?

A spinning wheel: Center = slow (almost no movement), Edge = fastest, Everything rotates together but moves differently.