Motion And Gravity Flashcards
Define 1 radian
The angle subtended at the centre of a circle with an arc length equal to the radius.
Length of arc (s) =
S = r ✖️theta
Length of arc = radius x angular displacement
Speed of circular motion =
Speed = angular velocity x radius (v = wr)
Angular velocity (w) =
Angular velocity = angular displacement / time
Acceleration (a) of circular motion =
a = Angular velocity x speed (a = wv) a = speed squared ➗radius (a = v^2 / r)
State Newton’s law of gravitation
Any 2 point masses attract each other with a force directly proportional to the product of their masses, and indirectly proportional to the square of their separation. (F = GMm / r^2)
Define gravitational field strength (and g = )
The gravitational force exerted per unit mass on a small object. (g = F/m ; g = Gm/r^2)
Define gravitational potential (omega)
The work done per unit mass in bringing a mass from infinity to a point. (= -GMm / r)
Kinetic energy in a gravitational field
k.e. = GMm/2r (from F = mvv/r = GMm/rr and k.e. = 0.5mvv)
Velocity of an orbiting object (v) =
V^2 = GM/r
The orbital period (T) =
T^2 = (4pi^2/GM)r^3
Define an oscillation
The repeated movement of an object back and forth on either side of an equilibrium position
Define free oscillations
The direct displacement of an object, causing it to oscillate at its natural frequency.
Define forced oscillations
Objects are forced to vibrate/oscillate at a forced frequency, due to vibrations from a secondary source.
Define the phase of an oscillating particle
The point that an oscillating particle has reached within 1 complete cycle.
Define simple harmonic motion
The motion of an oscillator in which acceleration is directly proportional to displacement, but in the opposite direction.
State the requirements for simple harmonic motion (s.h.m.)
- A mass that oscillates
- A position where the mass is in equilibrium
- The presence of a restoring force which brings the mass back to a rest position (force is directly proportional to displacement, but in the opposite direction
Angular frequency (w) =
W = 2pif
State the defining equation of s.h.m. (a = )
a = -w^2 x
Define damping
When the amplitude of oscillations decays exponentially over time, due to the effect of external forces.
Define critical damping
The minimum amount of damping required to return an oscillator to its equilibrium position without oscillating (so oscillations die out immediately).
Define resonance
When an oscillating system is forced to vibrate at its natural frequency, resulting in the maximum possible amplitude.
State the characteristics of resonance
- Natural frequency = driving frequency
- Maximum amplitude
- Absorbs the greatest possible energy from driver
