Circular Motion Flashcards
define angular velocity
ω, the rate of change of angular displacement*
*angle swept in a second
angular velocity
ω= θ/t
ω= rad s-1
θ= rad
define angular displacement
angle swept through in one second
angular displacement
s=rθ
θ= angular displacement
s= arc length
angular speed
v = s/t = rθ/t = rω
linear velocity
v = ωr
why would an object moving with constant speed be accelerating
the direction the object is moving in is continuously changing, therefore velocity is changing -> acceleration
periodic time, T
T= s/v = 2π/ω
frequency, f
f= 1/T = ω/2π
define periodic time
the time taken for particle to travel once around the circle
define frequency
number of revolutions made per second
what direction is acceleration
always towards the centre of the circle
centripedal acceleration
a = vω = v²/r = rω²
what is the direction of force
always towards the centre
centripedal force
F = ma = mvω = mv²/r = mrω²
importance of centripedal force
without it, object would move in a straight line along tangent (centripedal force disappears when object moves in a line)
motion in a vertical circle
how to calculate tension at the top of the circle
T and mg are the same direction so:
T + mg = mv²/r
∴
T = mv²/r - mg
motion in a vertical circle
how to calculate tension at bottom of the circle
T and mg going opposite direction so:
T - mg = mv²/r
∴
T = mv²/r + mg
motion in a vertical circle
where is tension the greatest
when object is at the bottom
motion in a vertical circle
how to calculate tension at right and left sides
mg is downwards ∴ does n ot effect tension:
T = mv²/r
motion is a vertical circle
how to calculate tension at NE and NW angles
T = mω²r - mg cos/sin*θ
*depending on where θ is
notion in a vertical circle
how to calculate tension at SE and SW
T = mω²r + mg cos/sin*θ
*depending on where θ is
motion at an angle
how to calculate tension
- resolve forces as at angle:
* horz: T cos/sinθ = mv²/r
* vert: T cos/sinθ = mg - use pythagorus to find T at angle
*depending on where θ is
motion at an angle
how to show it is not possible for string to be horizontal
T sinθ/ T cosθ = tanθ = mg/mv²÷r or gr/v²
motion at an angle
why can the string never be horizontal
θ must be 0 ∴ tanθ = 0 –> for this v² must be infinite (not possible)
how to convert radians-degrees
° => rad
times by π/180
rad => °
times by 180/π
