Download PHY 303k Test 2 Formula Sheet 1. Values of

PHY 303k Test 2 Formula Sheet
1. Values of√ Trigonometric Functions
√ (angle in degrees): cos(0) = sin(90) = 1, cos(30) =
sin(60) = 3/2, cos(45) = sin(45) = 2/2, cos(60) = sin(30) = 1/2, and cos(90) = sin(0) = 0.
2. Momentum Principle: F~net = d~p/dt = m~a. If F~net is constant, F~net = ∆~p/∆t. (Remember, d~p/dt,
or equivalently m~a, describes the response of the system to the net force acting on it.)
3. Energy Principle (without heat exchanges): ∆E = Wsurr .
4. Kinematics (constant ~a or constant α):
• ~r = ~r0 + ~v0 t + 1/2~at2 and ~v = ~v0 + ~at.
• θ = θ0 + ω0 t + 1/2αt2 and ω = ω0 + αt.
q
5. Relativistic Factor: γ ≡ 1−(|~v1|/c)2
6. Momentum:
• Relativistic: p~ = γ m~v
• Non-Relativistic: p~ = m~v
7. Energy for a Single Particle:
• Relativistic: E = γ mc2 = mc2 + K where mc2 is the rest energy and K is the kinetic energy.
• Non-Relativistic: E = K = 1/2mv 2 where K is the kinetic energy.
8. Forces:
• Gravitational: F~grav = − Gm|~r1|2m2 r̂.
• Spring Force: The force an ideal spring exerts on a mass is Fs = −ks sL̂ where ks is the force
~ − L0 , L0 is the equilibrium length of the spring and L
~ is the
constant for the spring, s = |L|
position of the mass relative to the point where the spring is anchored.
• Frictional Force: is directed opposite the motion that would occur if friction were not present.
– Kinetic Friction: |fk | = µk FN where µk is the coefficient of kinetic friction and FN is the
force normal to the surface.
– Static Friction: |fs | ≤ µs FN where µs is the coefficient of static friction and FN is the force
normal to the surface.
9. Circular Motion:
• Fnet,radial = maradial = mv 2 /r towards the center of rotation.
• s = rθ where s is arclength so v = rω where v is tangential speed and ω is the angular speed.
• If v is constant ω = 2π/T and T = 2πr/v where T is the period.
~·B
~ = Ax Bx + Ay By + Az Bz = |A||
~ B|
~ cos θ, where θ is the angle b/w the vectors.
10. Dot Product: A
R
11. Work (mechanical energy transfer): W = F~ · d~r. If F~ is constant, W = F~ · ∆~r
12. Work and Potential Energy: ∆UF = −WF where WF is the work done by force F~ and ∆UF is
the change in the potential energy function associated with the force F~ .
• Spring Potential Energy: Us = (1/2)kx2 where x is displacement relative the spring’s relaxed
length.
(F/A)
13. Young’s Modulus: Y = (∆L/L)
= kdi where F/A is the applied force per area, (∆L/L) is the
fractional change in length, ki is the interactomic spring constant, and d is the interatomic spacing.
14. Simple Harmonic Oscillator: The equation m(d2 x/dt2 ) = −kx p
has the solution x = A cos(ωt + φ)
or equivalently x = A sin(ωt + θ) where A is the amplitude, ω = (k/m) is the angular frequency,
and φ or θ is the phase angle.