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angular motion - Coggle Diagram
angular motion
Uniform motion
is called uniform motion when angular acceleration is constant
ωf= ωi+ αtωf2=
ωi2+ 2 α(θf -θi)
θf= θi + ωit + 12αt2
3 equations of rotational motion with constant angular acceleration
Wi = initial angular velocity
Wf = final angular velocity
a = angular acceleration (rad/s^2)
θi = initial angular displacement (rad)
θf = final angular displacement (rad)
t = time (s)
relationship between linear and angular motion
Linear motion is one-dimensional motion along a straight line. In linear motion, an object will move in one direction
s = r θ
v = r ω
at= r α
an= r ω2= 𝑣𝑣2
An = normal or centripetal acceleration (m/s^2)
centripetal acceleration always points towards the center of the circle, whereas tangential acceleration acts tangent to the circle, meaning it changes the object's speed, not its direction.
s = linear displacement [m]
at= tangential acceleration [m/s2]
v = tangential velocity [m/s
α= angular acceleration [rad/s2]
ω= angular velocity [rad/s]
θ= angular displacement [rad]
r = radius of rotation [m]
Definition
ANGLE DISPLACEMENT
is defined as the angle and the direction through which a body turns
Measure using rad or revolution
1 revolutuion = 360 degrees = 2(6.283) radians
ANGULAR VELOCITY
Is defined as the rate of change of angular displacement with respect to time
W = dθ/dt
W= angular velocity (rad/s)
θ = angular velocity (rad)
t = time(s)
d = difference
measured using rad/s
Can also be represented as rev per min (rpm)
1 RPM = 2(6.283)/60 rad/s
Angular acceleration
Is difend as the rate of change of angular velocity with respect to time
a = dw/dt or d^2θ/dt^2
a = angular acceleration (rad/s^2)
w = angular velocity
θ = angular displacement (rad)
t = time (s)
measure using (rad/s^2)