TRANSLATIONAL AND ROTATIONAL MOTION

Translational motion

occurs when an object changes position from one point to another

Rotational motion

happens when an object spins around an axis

A basketball player running across court

example of translational motion

A windmill spinning

example of rotational motion

Displacement

the change in the object's position or direction and can be denoted as Δx, Δy, or Δz depending on the axis

Displacement formula & unit

Δx = xf - xi (displacement = final position - initial position), m

Δ

delta symbol (means change or difference)

Δx

displacement

Δv

velocity change

Δt

time interval

Speed

how fast an object moves

Speed formula & unit

speed = distance ÷ time, m/s

Velocity and its formula & unit

how fast an object moves in a particular direction, vf = vi + at, m/s

Acceleration formula & unit

acceleration = change in velocity ÷ time, m/s²

Force formula & unit

F = ma, N (newton)

Average velocity

describes how fast an object moves and equals the rate at which its position changes over time

Average velocity formula and unit

Vave = Δx ÷ Δt, m/s

Average acceleration

measures the overall change in an object's velocity divided by the total time taken

Angular quantities

describe rotational motion around an axis, serving as the counterpart to translational motion's linear motion variables

θ

difference in

Angular displacement

the angle through which an object rotates around a specific center or axis

Angular displacement formula and unit

Δθ = θ - θ₀, rad

Angular velocity

the rate at which an object rotates or spins around a central point or axis

Angular velocity formula and unit

ω = Δθ ÷ Δt, rad/s

Angular acceleration

the rate at which an object's rotational speed and direction change over time

Angular acceleration formula and unit

α = Δω ÷ Δt, rad(s)^2

Torque

turning effect of a force

Torque formula and unit

t = F x r, N·m (newton-meter)

F

magnitude of the applied force

r

distance from the pivot point to where the force is applied (lever arm)