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Angular Motion - Coggle Diagram
Angular Motion
Uniform Motion
Angular acceleration is constant
ωf = ωi + αt
ωf^2 = ωi^2 + 2a(θf - θi)
θf = θi + ωi t + 1/2(at^2)
ωi = initial angular velocity [rad/s]
ωf = final angular velocity [rad/s]
α = angular acceleration [rad/s^2]
θi = initial angular displacement [rad]
θf = final angular displacement [rad]
t = time [s]
Angular Velocity
Rate of change of angular displacement with respect to time
ω = 𝑑θ/dt
ω = Angular Velocity (rad/s)
θ = angular displacement (rad)
t = time (s)
Measured using rad/s or rpm
1 rpm = 2π/60
Angular Acceleration
Rate of change of angular velocity with respect to time
a = 𝑑ω/dt or d^2θ/dt^2
a = angular acceleration (rad/s^2)
ω = angular velocity (rad/s)
θ = angular displacement (rad)
t = time (s)
Angular Displacement
Defined as the angle and direction through which a body turns
Measured using rad or revolution
Denoted by θ
Relationship between Linear and Angular motion
Equations
s = r θ
v = r ω
at = r α
an = rω^2 = v^2/r
Units
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/s^2]
α = angular acceleration [rad/s^2]
an = normal or centripetal acceleration [m/s^2]