6.1 Periodic motion Flashcards
Define Uniform Circular Motion.
When an object is moving in a circular path at a constant speed.
What is the resultant force called in this scenario?
Centripetal force
What is the equation(s) for centripetal force?
What do the letters represent in this equation?
What direction does the centripetal force act in?
Towards the centre of the circle
Why is the object accelerating when its speed is constant?
Centripetal force acts perpendicular to the direction of motion, and so constantly changes the direction of the velocity vector.
Define centripetal acceleration.
Acceleration of an object moving in a circular path.
What is the equation(s) for centripetal force?
What do the letters represent in this equation?
What direction does the centripetal acceleration act in?
Towards the centre of the circle
(Same direction as the centripetal force, since F=ma)
Define angular displacement?
The angle an object moves through as it travels along a circular path
(The angle in radians)
Define arc length.
The distance an object moves through as it travels along a circular path.
What do the letters represent in this equation?
Define the radian.
1 radian is when s=r in the arc length equation.
1 radian = 57.3 degrees
How can you convert from radians to degrees?
Think of the 180 being in units of degrees and the pi being in units of radians
How can you convert from degrees to radians?
Think of the 180 being in units of degrees and the pi being in units of radians
What is the equation for the cirfumference of a circle?
What do the letters represent in this equation?
What is the equation for the linear speed around the circumference of a circle?
What do the letters represent in this equation?
Define angular speed.
Is the angle an object moves through unit time.
What do the letters represent in this equation?
What other equation(s) can angular speed be written in?
Can you see the similarities with linear speed?
What do the letters represent in this equation?
What are the conditions for SHM?
Acceleration is directly proportional and in the opposite direction to displacement.
What is the constant of proportionality in the SHM condition?
What is the displacement of an object undergoing SHM?
What do the letters represent in this equation?
What is the velocity of an object undergoing SHM?
What do the letters represent in these equations?
What is the acceleration of an object undergoing SHM?
And force would be this multiplied by m.
What do the letters represent in these equations?
What does it mean for an object to oscillate?
(To move in SHM)
Object moves, repeatedly, one direction then in the opposite direction through its equilbrium position.
Why do we refer to the resultant force in SHM as the restoring force?
Because it wants to restore equilibrium.
Hence it always points towards the equilibrium position.
What are the 2 main examples of a Simple Harmonic Oscillator?
- Mass-spring system
- Simple pendulum
What is the graident of a velocity-time graph?
Acceleration.
What is the restoring force in a mass-spring system?
aka Hooke’s law
What do the letters represent in this equation?
What is the equation for maximum speed?
What do the letters represent in this equation?
What is the restoring force in a simple pendulum?
What do the letters represent in this equation?
What is the equation for maximum acceleration?
What do the letters represent in this equation?
Why are both these restoring forces negative?
Because they act in the opposite direction to the displacement.
ie they act towards the equilibrium position.
Where in an oscillation does the maximum speed occur?
At the equilibrium position.
What are the frequency and time period equations for the mass-sping system?
What do the letters represent in this equation?
Where in an oscillation does the zero speed occur?
At maximum displacement (Amplitude).
What are the frequency and time period equations for the simple pendulum?
What do the letters represent in this equation?
Where in an oscillation does the maximum acceleration occur?
At maximum displacement (Amplitude).
Is the time period of a mass-spring system independent of gravity?
Yes.
Gravity doesn’t appear in the equation
Where in an oscillation does zero acceleration occur?
At the equilibrium position.
Is the time period of a simple pendulum independent of amplitude?
Yes.
Amplitude does not appear in the equation (but only for small angles).
What is the equation for elastic potential energy for a mass-spring system?
What do the letters represent in this equation?
What is the equation for maximum elastic potential energy for a mass-spring system?
and hence total energy
What do the letters represent in this equation?
Using the previous 2 equations, give an equantion for KE.
What do the letters represent in this equation?
Draw a graph of energy vs displacement with KE, EPE, and total energy.
Draw a graph of energy vs time with KE and EPE.
Define damping.
When an oscillating system loses energy. Resulting in lessened amplitude.
What are the 4 types of damping?
- Light damping
- Heavy damping
- Critical damping
- Over damping
What is light damping?
When the amplitude is gradually decreased by a small amount each oscillation.
What is heavy damping?
When the amplitude is decreased by a larger amount each oscillation.
What is critical damping?
When the amplitude is reduced to zero in the shortest possible time (without oscillating).
What is over damping?
When the amplitude is reduced slower than with critical damping, but without any oscillations.
Define free vibrations?
Involve no energy trasfer to or from surroundings. The oscillator will oscillate at its natural/resonant frequency.
Define force vibrations?
Involve an external driving force, driving an oscillator at a specific driving frequency.
Define resonance.
Is when the driving frequency appraoches the natural frequency. The oscillator gains more enegry and hence oscillates with increasing amplitude.
What does a resonance graph look like?
What effect does damping have on a resonance curve?
The curve becomes blunted, and the resonant frequency drifts lower than the natural frequency.
