Translational and Rotational Motion Quantities

Displacement

The straight-line change in an object’s position from its initial point (x₀) to its final point (x).

Change in x = x-x0 = meters

Formula for displacement

Velocity

The rate at which an object’s position changes over time. It indicates both how fast an object moves and in what direction.

Vave = change in x/change in t = m/s

Velocity formula

Acceleration

The rate of change of linear velocity over time. An object _______ if it speeds up, slows down, or changes its direction of motion.

Aave = change in velocity/change in time = m/s²

Formula for acceleration

Force

An interaction (a push or pull) applied to an object that causes it to change its velocity and accelerate in a straight line.

F=ma=N

Formula for Force

Angular DIsplacement

The angle through which an object rotates around a fixed axis from its initial angular position to its final position.

Angular Displacement = final angle - initial angle = rad

Formula for angular displacement

Angular Velocity

The rate at which an object rotates or spins around an axis over time. It measures how fast the rotation angle changes.

w = change in angle/change in time = rad/s

Formula for Angular Velocity

Angular Acceleration

The rate of change of angular velocity over time. It measures how fast an object spins up or slows down its rotation.

a = change in w/change in time = rad/s²

Angular Acceleration formula

Torque

The turning effect of a force.

t = rFsin() = N.m

Torque Formula