periodic motion Flashcards
angle in radians =
arc length / radius of circle
how many radians in a full circle
2π
what is angular speed
the angle an object rotates through per second
formula for angular speed
ω(rads^-1) = θ/t
ω = v/t
angular speed (rads^-1) = linear speed (ms^-1) / radius of circle of rotation (m)
frequency of circular motion
number of complete revolutions per second ( revs^-1 or Hz )
period of circular motion
time taken for a complete revolution in seconds
formula for angular speed including frequency
ω = 2πf
derived:
f = 1/T
ω = 2π/T
replace 1/T with f
ω = 2πf
what is centripetal acceleration
when velocity is changing since direction is changing
always directed towards the centre of the circle
formula for centripetal acceleration including angular speed
a = ω^2r
newton’s first law of motion
an object’s velocity will remain the same unless an external force acts upon it
why must the centripetal force exist?
an object travelling in a circle has a centripetal acceleration
due to newton’s first law there must be a force causing this acceleration
formula for centripetal force
F = mω^2r
derived:
F =ma
a = ω^2r
what keeps an object moving in a circle
the centripetal force
if removed the object would fly off at a a tangent with velocity v
formula for centripetal acceleration
a = v^2/r
what does it mean to say an object is moving with simple harmonic motion
it oscillates to and fro either side of an equilibrium position
equilibrium position is the midpoint of the object’s motion
