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Kinematic (Angular Motion) - Coggle Diagram
Kinematic (Angular Motion)
Definition
Angular Displacement
measured using radian [rad]
1 revolution = 360 degree = 2π radians
denoted by θ
it is defined as the angle and the direction through which a body turns
Angular Velocity
measured using radian per second [rad/s] or revolution per minute [rpm]
denoted by ω
it is the rate of change of angular displacement with respect to time
Angular Acceleration
measured using radian per square second [rad/s^2]
denoted by a
it is the rate of change of angular velocity with respect to time
Formulae for constant angular acceleration
ωf = ωi + α t
ωf^2 = ωi^2 + 2 α (θf - θi)
θf = θi + ωi t + 1/2α t^2
ωi = initial angular velocity [rad/s]
ωf = final angular velocity [rad/s]
α = angular acceleration [rad/s2]
θi = initial angular displacement [rad]
θf = final angular displacement [rad]
t = time [s]
Relationship with linear motion
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]
s = r θ
v = r ω
at = r α
an = r ω^2 = 𝑣^2/r
A rolling ball has translational motion and rotational motion
Translational Motion:
Every particle in the rigid body has the same instantaneous velocity (no rotation)
Rotational Motion:
Every particle in the rigid body has the same angular velocity and travels in circle around a fixed axis
