Mechanics and Special Relativity Flashcards
What is A•B physically?
The magnitude of A multiplied by the component of B in the direction of A.
What A•B mathematically?
|A||B|cosx
Is A•B = B•A?
Yes
A•B in terms of components?
AxBx + AyBy + AzBz
A•A=?
(|a|)^2
What is Einstein’s first postulate?
The laws of physics are the same in every inertial frame of reference.
What is Einsteins second postulate?
The speed of light in vacuum is the same in all inertial frames of reference and is independent of the source.
What is the speed of light?
2.998x10^8
What 3 conclusions are drawn from Einsteins postulates?
- No absolute ruler length
- No absolute clock
- Simultaneity depends on the observers.
What is the Lorentz factor (equation)?
Y=(1-(u/c)^2)^-1/2
Do moving clocks tick fast or slow?
Slow
Time dilation equation
t=y•t0
Why can massive objects not move at the speed of light?
Because it would require infinite energy.
What is proper time?
Time as measured by an observer with a stationary clock (at the same location as the observer).
What is proper length?
The length of a body in a reference frame at which the body is at rest.
Do moving bodies contract or lengthen according to a stationary observer?
Contracts
Equation of length contraction?
L = L0/Y
How are lengths parallel and perpendicular to the direction of motion affected?
Parallel - contracted by factor of 1/y
Perpendicular - unaffected
What is a unit vector?
A vector that has magnitude 1
What’s Newton’s first law?
In the absence of a net force a body at rest will remain at rest, bodies in uniform motion will remain in uniform motion at constant velocity.
What’s Newton’s second law?
F=ma
What’s Newton’s third law?
For every action, there is an equal and opposite reaction.
Evaluate the frictional force on a body.
F = uN in opposite direction to direction of motion.
Which is bigger? Coefficient of friction when static or in motion?
Static
Fluid resistance at low velocity?
F = kV where k is viscosity
Fluid resistance at high velocity?
F = DV^2 where D is drag.
Work done =?
Wd = S F•ds
Path
How is the work done on an object and its kinetic energy related.
Wd = 🔼KE
What’s Hooke’s law?
Force on a mass due to a spring = -kx
What is the potential energy of a spring compressed or stretched by x from equilibrium?
U = (kx^2)/2
What is the speed of a mass compressed or stretched by X from equilibrium when it passes through equilibrium after release?
V=X•sqrt(k/m)
Equation of momentum?
P=mv
How does force affect momentum?
F = dP/dt
What is impulse?
🔼P = F x 🔼t for small 🔼t
What is a perfectly elastic collision?
Bounce off, KE is conserved
What is a perfectly inelastic collision?
Stick together, energy dissipated into deformation.
Velocity of the centre of mass =?
V = Ptotal/M
What is the change in velocity of rocket of mass M ejecting gas of mass m at speed v?
🔼V = mv/M-m
What is the acceleration of a rocket that is constantly ejecting gas at rate of dM/dt = c?
a= - vgas/M * c
Calculate angular frequency from linear speed and radius
w = V/r
Calculate the frequency of rotation from the angular frequency.
f=w/2pi
What is the centripetal acceleration of an object (equation)?
a = w^2*r towards centre of circle
What is the acceleration of a mass oscillating on a spring?
a = -kx/m
For a small x what’s the approximation for cosx?
1 - x^2/2
For small X what’s the approximation of sinx?
X
What’s the angular frequency of a pendulum of length L?
w = sqrt(g/L)
What’s the frequency of a pendulum of length L?
T = 2pi*sqrt(L/g)
What is a physical pendulum?
Any real pendulum that uses an extended body.
What is the angular frequency of a physical pendulum?
w = sqrt(I/mgd) where I is moment of inertia and d is distance from rotational axis to centre of gravity.
What is the force on a mass undergoing damped SHM?
F = -kx -bV
What is the decay timescale in damped SHM?
The time for the amplitude to be reduced by a factor of e.
What is the angular frequency of a slightly damped oscillator?
w’ = sqrt(k/m - b^2/4m^2)
What is the amplitude of a forced oscillator?
A = ______F_max_______________
Sqrt((k-mw^2)^2 + (bw)^2
Where w is driving angular frequency and b is the damping constant.
What is the classical mechanics limit?
V
