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Angular motion - Coggle Diagram
Angular motion
Relationship between linear & rotational motion
s = r θ
v = r ω
at= r α
an= r ω2= 𝑣𝑣2𝑟𝑟
wherer = 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]
Uniform motion
ωf= ωi+ αt
ωf2= ωi2+ 2 α(θf -θi)
θf= θi + ωit + 12αt2
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]
Angular Acceleration
α= 𝑑ω/𝑑𝑡or 𝑑^2θ/𝑑𝑡^2
α= angular acceleration [rad/s2]
ω= angular velocity [rad/s]
θ= angular displacement [rad]
t = time [s]
denoted as rad/s^2
Angular Velocity
ω= 𝑑θ/𝑑𝑡
ω= angular velocity [rad/s]
θ= angular displacement [rad]
t = time [s]
1 rpm = 2π/60rad/s
Unit conversion
1 revolution = 360 degrees = 2π radians = 6.284 rad
rpm = 2𝜋𝜋60rad/s = 0.1047 rad/s
1 rev X 2π = 6.283rad
1 rad / 2π = 0.16 rev
e)20⁰ = 0.349 rad
Angular Displacement
rad or revolution
denoted by θ
1 rev = 360 deg = 2πradians
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 circles around a fixed axis.