Section 6.1 - Further Mechanics Flashcards
What is uniform circular motion?
When an object is rotating at a steady rate
What is the speed for a point on the perimeter of a circle?
v = 2πr/T
Formula for angular displacement in terms of T?
θ = 2πt/T
Formula for angular displacement in terms of f?
θ = 2πft
What is angular speed?
The angular displacement per second
Formula for angular speed?
ω = 2π/T
or
ω = 2πf
What is the unit for ω?
rad/s
Formula for velocity in terms of ω
v = ωr
What unit is used for measuring angles?
Radians
Formula for the arc length?
S= θr
Why is an object moving in a circle at constant speed always accelerating?
- Because it has a constantly changing velocity
- Due to the constantly changing direction
- As there is a change in velocity there is a centripetal acceleration
What is the formula for centripetal acceleration?
a = v²/r
or
a = rω²
Why must there be a centripetal force acting on an object moving in a circle at constant speed?
- Because there is a centripetal acceleration.
- There must be a resultant force acting on the object to makign it accelerate.
What direction does the centripetal force act in?
Towards the centre of the circle
What is the equation for centripetal force?
F=mv²/r
or
F=mrω²
Define amplitude
The maximum displacement from the equilibrium postion
What are free vibrations?
Oscillations where the amplitude is constant and are not affected by frictional forces.
What is time period?
The time taken for one complete oscillation to occur
What is frequncy?
The number of cycles made by an oscillating object
What is the formula for angular frequncy?
ω = 2π/T = 2πf
Formula for the phase difference bewteen two objects oscillating at the same frequency?
2πΔt/T
Definition for SHM
Oscilating motion in which the acceleration is:
* Proportional to the displacement
* Always in the opposite direction to the displacement
* a α -x
What is the formula for aceleration?
a = -ω²x
What is the formula for displacement?
x = Acos ωt
What are the two formula for velocity?
v = -Aωsin ωt
or
v = ± ω √(A²-x² )
What is the max velocity?
Vmax = Aω
What are the two formula for acceleration?
a = -A ω²cos ωt
or a = -ω²x
What is the maximum acceleration?
a max = A ω²
Formula for time period of a mass-spring system?
T = 2π √(m/k)
Formula for time period of a simple pendulum
T = 2π √(l/g)
What does the energy v displacement graph look like?
- Potential energy is a parabolic shape
- Kinetic energy is an inverted parabola
- straighline for total energy
When is motion said to be damped?
When dissipasive forces are present
What is light damping and give an example?
- The amplitude gradually decreases by a small amount each oscillation
- Displacing a pendulum and letting it come to a stop naturally
What is critical damping and give an example?
- reduces the amplitude to zero in the shortest possible time after it has been displaced from equilibrium and released.
- Suspension in a car
What is heavy damping and give an example?
- the amplitude reduces slower than with critical damping, but also without any additional oscillations.
- Soft close door
What does the displacement time graph look like for each type of damping?
Check notes
What is a periodic force?
A force applied at regular intervals
What are forced vibrations?
Forced vibrations are where a system experiences an external driving force which causes it to oscillate
When does resonance occur?
When the forced vibrations are applied at the natural frequency
What is the resonant frequency?
The frequncy at which the maximum amplitude occurs
What happens to resosant frequency as the damping that is applied gets stronger?
It gets smaller (shifts to the left)
What happens to amplitude as the damping that is applied gets stronger?
It decreases
What is the y-int on a resonance graph?
The amplitude of the vibrataion generator
2 Applications of resonance?
- Radios - These are tuned so that their electric circuit resonates at the same frequency as the desired broadcast frequency.
- Musical instruments An instrument such as a flute has a long tube in which air resonates, causing a stationary sound wave to be formed.
Describe and Explain
Circular motion
- Acceleration is perpendicular to the magnitude of the tangential velocity
- ω = θ/t = 2π/t = 2πf
- v = 2πr/T = ωr
- a = v²/r = rω²
- f = mv²/r = mrω²
Describe and Explain
SHM
- Acceleration is proportional to displacement and toward the equilibrium position
- Acceleration velocity and displacement are sinusoidal with respect to time
