Kinematics (angular motion)

Definition

Formulae

angular velocity

angular displacement

angular acceleration

measure using rad

1 rev = 360 deg = 2pi rad

denoted by theta

It is defined as the angle and the direction through which a body turns

denoted by w

measured using rad/s or rpm

It is the rate of change of angular displacement with respect to time

measured using rad/s^2

denoted by a

It is the rate of change of angular velocity with respect to time

constant angular acceleration

image

relationship with linear motion

where

image

r = radius of rotation [m]

s = linear displacement [m]

θ = angular displacement [rad]

v = tangential velocity [m/s]

ω = angular velocity [rad/s]

at = tangential acceleration [m/s2]

α = angular acceleration [rad/s2]

an = normal or centripetal acceleration [m/s2]

motion

Translational

Rotational

Every particle in the rigid body has the same instantaneous velocity.

Every particle in the rigid body has the same angular velocity and travels in circles around a fixed axis.

Rolling

Translational + Rotational = Rolling