circular motion and simple harmonic motion Flashcards
define radian
the angle subtended at the centre of a circle when the arc length is equal to the radius`
define time period
the time taken for an object to complete 1 full circular orbit
define frequency
the number of circular orbit completed per second
stratergies to improve the accuracy of time period measurements
allow the object to settle by allowing it to complete a few circles
time 10 full circular orbits and then divided by 10
complete 3 measurements of time period and calculate an average
place a fiducial marker to mark the start and end of circular orbits
use a motion sensor with a data logger to measure many swings and analyse how period changes over time
define and calculate angular velocity
the number of radians swept by the radius of an object in circular motion per second
w = 2π/T = 2πf
describe the condition of uniform circular motion
when an object travels at constant speed with the resultant force always directed towards the centre
convert between angular velocity and tangential velocity
v = 2πr / T = wr
define and calculate centripetal acceleration
when the acceleration is always directed towards the centre of the circular orbit
a = v^2 / r = w^2r
calculate centripetal force
(assuming objects mass is constant)
F = ma = mv^2 / r = mw^2r
practically demonstrate the relationship between radius and time period
select a radius of orbit by measuring out a length of string with a fixed mass hung on the other end to create a centripetal tension force and whirl it around your head in uniform circular motion
let the mass settle for 2 full orbits and start timing when the mass passes by a fiducial marker. Measyre the time for 10 complete oscillations and divide by 10 to get the time period. Repeat this process twice for this length and then repeat the whole process for 6 more lengths
Plot a graph of T^2 against r which should be a straight line passing through the origin as the mass and tension force are constant
F = mw^2r = (m4π^2 / T^2) x r
=> T^2 = (m4π^2 / F) x r
define displacement
how far the object is from the equilibrium position measured in metres (for a pendulum angular displacement can be given in radians)
define amplitude
the maximum displacement of the object from the equilibirum position measured in metres
define time period
the time taken to complete 1 full oscillation
define frequency
the number of complete oscillations per second
define angular velocity
the number of radians per second travelled by the object
define phase difference
the difference between 2 points on a wave function expressed as an angle
calculate angular frequency
w = 2π / T = 2πf
define simple harmonic motion
when the magnitude of the acceleration is directly proportional to the displacement but in the opposite directione
strategies to improve the accuracy of time-period measurements
allow the oscillations to settle before starting timing
time 10 full oscillations and then divided by 10
complete 3 measurements of time period and calculate average
place a fiducial marker to mark the start and end of oscillations at the equilibrium position
use a slow motion video camera
show that an object will be in simple harmonic motion if its displacement can be expressed as x = Acos(wt) or x = Asin(wt)
a = -w^2x
=> derivative of x / t = -w^2x
there are 2 functions where their 2nd derivative is -w^2 times the original function which are: cosine and sine
=> if x = Acos(wt), a = -Aw^2cos(wt) = -w^2x
=> if x = Asin(wt), a = -Aw^2sin(wt) = -w^2x
describe the energy changes starting from maximum displacement for a pendulum
the pendulum starts with maximum GPE which is transferred to kinetic energy and the equilibrium position and then back t GPE. This whole process repeats as it swings back towards the starting position, finishing with GPE.
describe the energy change starting for maximum velocity for a mass-spring system
the mass starts with maximum kinetic energy which is transferred to elastic potential energy at maximum displacement which is then transferred back to kinetic energy as the mass comes back to the equilibrium position. This process then repeats in the opposite direction finishing back with kinetic energy at the equilibrium position
define free vibration
when an oscillating sytem experiences no external force so mechanical energy is constant
define damped vibration
when an oscillating system experiences an external force acting to decrease the mechanical energy
define forced vibration
when a system has a periodic external force applied to it
desrcribe the effects of damping on an oscillating sytem
the damping force will act in the opposite direction to the velocity, decreasing the mechanical energy and therefore decreasing the amplitude and maximum velocity
define resonance
when a system is subjected to a periodic external force with a frequency equal to the systems natural frequency
define natural frequency
the frequency at which a system would oscillate if given an initial displacement and then allowed to oscillate freely
describe the observation from a batons pendulum with 1 pendulum providing a periodic driving force and 3 other connected pendula that are shorter, the same length and longer length than the driving pendulum
pendulum y has the same length as pendulum p and therefore has the same natural frequency as p. therefore y will be in resonance, have much larger amplitude and will oscillate with its displacement 90 degrees out of phase with the driving pendulum displacement.
pendulum x has a shorter length than p, therefore it has a larger natural frequency than P and so will be forced to oscillate below its natural frequency with a small amplitude and its displacement will be in phase with pendulum p.
pendulum z has a longer length than P, therefore it has a smaller natural frequency than P and so will be forced to oscillate above its natural frequency with a small amplitude and its displacement will be in anti phase with pendulum p.,
How can a graph of a over be correct
Straight line through origin showing a µ x
