物理笔记
Preface
The post is the note based on the textbook Fundamentals of Physics written by David Halliday, Robert Resnick and Jearl Walker (ISBN: 978-1-118-23072-5)
Some particular symbols are introduced to describe some properties, as listed below.
Symbol Table
| Symbol | Meaning |
|---|---|
| 🎒 | Already learned in middle school |
| ⚠ | Key point of some contents |
The post is done individually by Ryker Zhu from Nanjing
University of Information Science and Technology, published under
the license CC
BY-NC-SA.
Measurement
| Symbol | Name | Quantity |
|---|---|---|
| \(s\) | second | time |
| \(m\) | meter | length |
| \(kg\) | kilogram | mass |
| \(A\) | ampere | electric current |
| \(K\) | kelvin | thermodynamic temperature |
| \(mol\) | mole | amount of substance |
| \(cd\) | candela | luminous intensity |
Motion
Vector & Scalar
flowchart LR
A(Physical Quantities) --- B(Vector Quantities) & C(Scalars)
B --- D(Magnitude) & E(Direction)
🎒 Component: Projection of the vector on an axis.
- Vector component : \(a_x\hat{i},\,a_y\hat{j}\)
- (Scalar) component : \(a_x,\,a_y\)
🎒 Scalar Product or
Dot Product: spoken as "a dot b" \[\vec{a}\cdot\vec{b}=a\cdot b \cos\phi\]
\(a\) - magnitude of the vector \(\vec{a}\);
\(\phi\) - angle between \(\vec{a}\) and \(\vec{b}\).
Vector Product or Cross Product: spoken as "a cross b"
Magnitude
\[c=a\cdot b \sin\phi\] \(c\) - magnitude of the vector \(\vec{c}\);
\(\phi\) - smaller of the two angles between \(\vec{a}\) and \(\vec{b}\).Direction
Perpendicular to the plane containing \(\vec{a}\) and \(\vec{b}\).
Determine with right-hand rule, right-hand fingers swap \(\vec{a}\) into \(\vec{b}\).
Position and Displacement
🎒 Kinematics: (/,kɪnɪ'mætɪks/ or /kaɪnə'mætɪks]/) Classification and comparison of motions.
🎒 Particle: Point-like object
Projectile Motion
A particle moves in a vertical plane with some initial velocity, but its acceleration is always the free-fall acceleration, which is downward.
Such a particle is called projectile /prəˈdʒektaɪl/ and its motion is called projectile motion.
Horizontal Motion: \[x-x_0=v_{0x}t=\left(v_0\cos\theta_0\right)t\] Vertical Motion: \[y-y_0=v_{0y}-\frac{1}{2}gt^2\]
The Equation of the Path (Trajectory /trəˈdʒektəri/): \[y=\left(\tan\theta_0\right)x-\frac{g}{2\left(v_0\cos\theta_0\right)^2}x^2\] The equation is also the one of parabola /pəˈræbələ/ so the path is parabolic.
Force
Newtonian Mechanics: The relation between a force and the acceleration it causes
🎒 Newton's three primary laws of motion
Net Force or Resultant Force: Adding all forces acted on the same body
Principle of superposition for forces: A single force that has the same magnitude and direction as the calculated net force would then have the same effect as all the individual forces.
⚠ Newton's laws is not always true unless in inertial /ɪˈnɜːʃl/ reference frames.
Newton’s First Law
If no net force acts on a body (\(\overrightarrow{F_\mathrm{net}}=0\)), the body’s velocity cannot change; that is, the body cannot accelerate.
Newton’s Second Law
The net force on a body is equal to the product of the body’s mass and its acceleration.
\[\overrightarrow{F_\mathrm{net}}=m\vec{a}\]
⚠ The acceleration component along a given axis is caused only by the sum of the force components along that same axis, and not by force components along any other axis.
Forces in Equilibrium: Any forces on the body balance one another, and both the forces and the body are said to be in equilibrium (/ˌiːkwɪˈlɪbriəm/ or /ˌekwɪˈlɪbriəm/).
Newton’s Third Law
When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.
Particular Forces
🎒 Normal Force
When a body presses against a surface, the surface (even a seemingly rigid one) deforms and pushes on the body with a normal force \(\overrightarrow{F_N}\) that is perpendicular to the surface.
🎒 Frictional force
The force on a body when the body slides or attempts to slide along a surface. The force is always parallel to the surface and directed so as to oppose the sliding. On a frictionless surface, the frictional force is negligible.
- If the body does not slide, the frictional force \(f_s\) is a static frictional
force.
- The magnitude of \(f_s\) has a
maximum value \(f_{s,max}\) given by
\[f_{s,max}=\mu_sF_N\]
- \(\mu_s\) - coefficient of static friction
- \(F_N\) - magnitude of the normal force.
- The magnitude of \(f_s\) has a
maximum value \(f_{s,max}\) given by
\[f_{s,max}=\mu_sF_N\]
- If there is sliding, the frictional force is a kinetic
frictional force.
- The magnitude of the frictional force rapidly decreases to a
constant value \(f_k\) given by \[f_k=\mu_kF_N\]
- \(\mu_k\) - coefficient of kinetic friction
- The magnitude of the frictional force rapidly decreases to a
constant value \(f_k\) given by \[f_k=\mu_kF_N\]
Drag Force
When there is relative motion between air (or some other fluid) and a body, the body experiences a drag force \(\vec{D}\) that opposes the relative motion and points in the direction in which the fluid flows relative to the body.
The magnitude of D: \[D=\frac{1}{2}C\rho Av^2\] - \(C\) - an experimentally determined drag coefficient - \(\rho\) - the fluid density (mass per unit volume) - \(A\) - the effective cross-sectional area of the body (the area of a cross section taken perpendicular to the relative velocity \(\vec{v}\)).