World in Physics


Force and motion




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.


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


method of dimensional analysis


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.



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

  • gravitational field (gravity)



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

Fluid and thermodynamics


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


  • 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.


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



Electricity and magnetism

Relativity and quantum physics

Philosophy Association Data Structure


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