PHY1001 quickcheck

week 6-7

1. torque $\tau = Fl = I_{cm}\alpha _{cm}$
2. angular acceleration
   1. $F_{tan} = m_1a_{tan},a_{tan}=ra_z$, l = r
   2. $\tau = F_{tan}r = m_1a_{tan}r = m_1 r^2 a_z$
   3. $\tau = \sum \tau _1 = \sum m_1 r^2 a_z = I a_z$
3. rigid body rotation about moving axis–axis choosing
   1. choose COM
   2. choose instant center
4. translation and rotation
   1. $\tau = Ia$ is under assumption that stationary axis
   2. if move, have to fufill following 2 condition
      1. be axis of symmetry
      2. axis not change dir. (gyroscope is not)
   3. Energy conservative method
      1. E = kinetic energy + rotation energy + gravitational potential = constant

week 8

1. equilibrium
2. center of gravity（重心，与质心mass区分）
3. regid body equilibrium problems
4. elasticity
   1. Young’s modulus Y (单面压缩)
   2. bulk modulus B （全面压缩）
   3. shear modulus S （剪切）

week 9

1. Newton’s law of gravitation
2. weight(重量，与质量mass区分)
3. gravitational potential energy
4. escape velocity and motion of satellites
5. kepler’s law
6. black hole
7. spherical mass distribution

week 10

1. density and pressure
2. pressure in a fluid at rest
3. pascal’s law
4. measuring pressure
5. buoyancy (浮力)
6. continuity of flow
7. bernolli’s law

week 11

1. oscillation–formula and definition
   1. definition
      1. basic definition need to know
         1. displacement from the equilibrium position EP 位移 x
         2. restoring force (N)–回复力 F
         3. amplitude (m)-max magnitude of displacement–振幅 A
         4. the angular frequency (rad/s) $\omega = \frac{2 \pi}{T} = 2\pi f = \sqrt{\frac{k}{m}}$ --角频率 $\omega$
         5. the period T (s) = $2 \pi \sqrt{\frac{k}{m}}$ --周期 T
         6. the frequency f (Hz) --频率 f
         7. phase constant (rad) $\delta$–相位常数
         8. phase $\omega t + \delta$ --相位
      2. relation between them
         1. amplitude A and phase can cal. by init
            1. by $x_{init}, v_{init}$, ratio, we get A and $\tan \delta$
         2. $\omega = \sqrt{\frac{k}{m}}$ angular frequency is important, make connection between a,v,x in diff. and int.
         3. f and T are indep. with A in SHM
         4. x,v,a have a $\triangle \delta = T / 4$
         5. phase are same map onto the circular motion, angular are real
      3. solve and fix amplitude and phase acc. to init. condition
   2. harmoic oscillation简谐振动
      1. SHM and circular motion
      2. simple harmonic motion
      3. circular and trigonometric function
      4. SHM energy
         1. E = K + U conserved
         2. use int. to evaluate the U and K per T(period)
   3. oscillation system
      1. method
         1. find (EP)
         2. identify physics formula related to the system
         3. obtain the equation of motion (EOM), and write in form that familiar
      2. verticle spring- $\exist$ downward force
      3. simple pendulum(mass consentrate on bottom–a point)
         1. max angular displacement $\phi = \phi _0 cos(\omega t + \delta)$
         2. angular frequency $\omega = \sqrt{\frac{g}{L}}$
         3. $T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{g}{L}}$
         4. indep. with amplitude
      4. physical pendulum(mass distrbute whole body)

$\omega = \sqrt{\frac{mgd}{I}} \\ \text{.} \\ T = 2 \pi \sqrt{\frac{I}{mgd}}$

  7. torsional oscillator (扭振子)

4. General motion near equillibrium (suppose x is small)
   1. it is advance topic
5. Damped oscillation (阻尼震动)
   1. alway have dissipative force(耗散力) e.g. resistance and friction
   2. we see the amptitude decrease, so we find how it decrease
   3. $x(t) = A_0 e^{-\frac{b}{2m}t} \cos (\omega t + \delta)$
   4. energy
   5. Q factor and decay time
   6. application of damped-automobile’s suspension system
6. Driven (Forced) Oscillation and Resonance (受迫振动)
   1. periodic force

week 12

1. wave
   1. wave in general
   2. Harmonic (sinusoidal) waves
   3. energy in wave motion
   4. principle of superposition(叠加)