Angular Motion Flashcards
linear motion vs angular motion
displacement = s (m) initial velocity = u (ms-1) final velocity = v (ms-1) acceleration = a (ms-2) time = t (s)
linear motion vs angular motion
angular displacement = w (rad) initial angular velocity = w₀ (rad s-1) final angular velocity = w (rad s-1) angular acceleration = α ( rad s-2) time = t (s)
w = dθ / dt
w = angular velocity (rad s-1) θ = angular displacement (rad) t = time (s)
w = v/r
w = angular velocty (rad s-1) v = linear velocty (ms-1) r = distance from axis of rotation (m)
w = 2π/ T
w = angular velocity (rad s-1) π = pi T = period of rotation (s)
since frequency, f = 1/T this equation could also be stated as
w = 2πf
w = angular velocity (rad s-1) π = pi f = frequency (Hz)
linear motion vs angular motion - equations
v = u + at s = ut + 1/2at^2 v^2 = u^2 + 2as s = 1/2 (u+v)t
linear motion vs angular motion - equations
w = w₀ + αt θ = w₀t + 1/2αt^2 w^2 = w₀^2 + 2αθ θ = 1/2(w₀ + w)t
T = time/revolutions
T = period (s)
θ = 2π x revolutions
θ = angular displacement (m) π = pi
Tangential Acceleration
aₜ = rα
of an object which is on a curved path
aₜ = tangential acceleration (ms-2) r = radius (m) α = angular acceleration (rad s-2)
Centripetal Acceleration
aᵣ = v^2/r and aᵣ = w^2r
of an object moving in a circular path towards the centre of axis of rotation.
aᵣ = centripetal acceleration (ms-2) r = radius (m) v = linear velocity (ms-1) w = angular velocity (rad s-1)
The direction of the centripetal acceleration is ALWAYS towards
the centre of the circle
and
is at right angles to the tangential acceleration
Centripetal Force
F = mv^2/r and F=mrw^2
F = Centripetal force (N) m = mass (kg) r = radius (m) v = linear velocity (ms-1) w = angular velocity (rad s-1)
Centripetal force = mgtanθ
Plane Banking
W =mg is balanced by the lift of an aeroplane.
When it banks it is at an angle this provides an upwards component to balance the weight and a centripetal component causing the plane to turn.
Conical Pendulum
\
|θ \ T
|___\
Tsinθ
Tcosθ = mv/r divide the two Tsinθ = mg divide the two tanθ = mv^2/r mv^2/r = F
tanθ = F/mg
F = Centripetal force mg = W
Centripetal radial or central force acting on an object is NECESSARY to
maintain circular motion and results in centripetal ACCELERATION of the object.
tensions direction will be found on the
and weights direction will be found on the
tensions - on the string
weight on the object
Why does an object travelling in a circular motion accelerate?
There is an unbalanced centripetal force acting on the object
would an object lose contact with a track if the mass is reduced and it travels at the same speed as before?
the car will not lose contact with the track.
As a smaller centripetal force is supplied by a
smaller weight.
To calculate the conical pendulum Tension, Weight or Fc you must
use Pythagoras’s theorem
w = θ/t
when given revolutions per minute
