World in Physics

一直认为物理是理科中最强大的学科,本学期取得了好成绩,再此想要好好地告别。量子与相对论带给了我思考的全新视角,希望我能借此更加理解这个世界。本文待完成。

Force and motion

Formulas

theorems

statics

conditions for equilibrium:

  • resultant force is $0$

  • no rotation: net torque must be $0$

that is, $F=0$ and $\tau{cw} =\tau{ccw}$.

Parallel-axis theorem

  • initial: rotating about CM.

  • final: parallel to the initial axis.

$I{parallel-axis}=I{CM}+md^2$

rotation matrix

  • two dimension:
  • three dimension:

(one example for rotating about the x-axis)

Projectile equation

Farthest distance for jumping:

$45$ degree.

efficiency of energy conversion

$20%$

method of dimensional analysis

example:

the change in gravitational potential energy

elastic collision

one-dimension elastic collision.
conservation of momentum and conservation of kinetic energy.

Rocket propulsion

  • vacuum

u: the constant velocity of the ejected burned gas relative to the rocket.

eliminated:

integrated:

the change of velocity of a rocket relates to the change of the rocket’s mass.

  • gravitational field (gravity)

expanded:

integrated:

the rocket will run faster if more mass of the burned fuel gas is expelled at a shorter time interval.

Fluid and thermodynamics

Formulas

Bernoulli’s equation

flow is conserved in a tube.

$C$: the coefficient of media resistance

thermal expansion

$\frac{\mathrm{d} L}{\mathrm{d} T}=\alpha L$,$\frac{\mathrm{d} A}{\mathrm{d} T}=2\alpha A$,$\frac{\mathrm{d} V}{\mathrm{d} T}=3\alpha V$

heat capacity

$C$: the amount of energy needed to raise the temperature of that sample by $1$ degree.

heat transfer $Q=C\delta T$

$c$: specific heat capacity. the heat capacity per unit mass.

$c=\frac{Q}{m\delta T}$,$Q=cm\delta T$

heat flow(heat transfer by conduction)
the amount of heat conducted per second: $P_c=\frac{K_cA}{L}(T_1-T_2)$
A: cross section area L: length K: coefficient of thermal conductivity

average kinetic energy of a partical: $\frac{1}{2}mv_{rms}^2=\frac{3}{2}k_BT$
rms: root mean square

examples

  • final temperature of mixture at thermal equilibrium

Let T be the final temperature of the system at thermal equilibrium. The total heat transfer is just 0.

substituting the values gives the T.

Theroems

how liquid wets container

attractive force between surface molecules and wall: adhesion

attractive force between surface molecules and liquid: cohesion

curved upward glass-water>water-water

curved downward glass-mercury<mercury-mercury

capillary effect

rise up: ad force is stronger against the weight of liquid

depress: ad is weaker than co

Wave

Optics

Electricity and magnetism

Relativity and quantum physics

Philosophy Association Data Structure

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