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Kinematics (Angular Motion) - Coggle Diagram
Kinematics (Angular Motion)
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 circles around a fixed axis.
Formulae for constant angular acceleration
ωf = ωi + α t
θf = θi +ωi t + ½ α t2
ωf2 =ωi 2 + 2α (θf - θi)
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
s = r θ
v = r ω
at = r α
an = r ω2 = 𝑣𝑣2
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]
Definitions
Angular Displacement
measured using radian (rad)
1 revolution = 360 degrees = 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 α
It is the rate of change of angular velocity with respect to time
