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p1047
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the-most-used-formulas-in-physics
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Secondary V
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Physics
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returning force
gravitational
spring returning constant
vergence
formula
formulas in physics
physics formulas
the acceleration
lenses
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Title (level 2)
Optics
Title slug (identifier)
optics
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Corps

The Equations of Spherical Mirrors and Lenses

​|M=\displaystyle \frac {h_{i}}{h_{o}} = \frac {-d_{i}}{d_{o}} = \frac {-l_{f}}{l_{o}} = \frac {-l_{i}}{f}|
 
|\displaystyle \frac {1}{d_{o}} + \frac {1}{d_{i}} = \frac {1}{f}|
 
|{d_{i}} = {l_{i}} + {f}|
 
|{d_{o}} = {l_{o}} + {f}|
 
|{l_{i}} \times {l_{o}} = {f}^2|
|f|: focal length (or focal distance)
|d_{o}|: object-mirror distance
|d_{i}|: image-mirror distance
|l_{o}|: object-focus distance
|l_{i}|: distance image-focus
|h_{o}|: pitch of the object
|h_{i}|: height of the image
|R|: radius of curvature
​|R = 2 \times {f}| (only in spherical mirrors)

 

Signs Convention for Mirrors

Measurement

Positive Sign

Negative Sign

Mirror-Image Distance

(|d_{i}|)
The image is real. The image is virtual.

Focal Length

(|f|)
The mirror is concave (convergent). The mirror is convex (divergent).
Magnification (|M|)
Image Height (|h_{i}|)
The image is upright. The image is upside down.

Signs Convention for Lenses

Measurement ​Positive Sign Negative Sign
Mirror-Image Distance (|d_{i}|) The image is real (on the opposite side of the lense to the object). The image is virtual (on the same side of the lense as the object).
Focal Length (|f|) The lense is convex (convergent). The lense is concave (divergent).
Magnification (|M|)
Image Height (|h_{i}|)
The image is upright. The image is upside down.

Refraction

Snell-Descartes Law of Refraction

​|n_{1}\times \sin \theta_{i} = n_{2}\times \sin\theta_{r}|

|n_{1}|: refractive index of environment 1
|\theta_{i}|: angle of incidence |(^{\circ})|
|n_{2}|: refractive index of environment 2
|\theta_{r}|: angle of refraction |(^{\circ})|

The Optical Power |(P)|

|P = \displaystyle \frac {1}{f}|

|P|: optical power of the lense in dioptres |\delta|
|f|: focal length (or focal distance) in metres |\text {(m)}|

The Optician's Equation

|P = (n - 1) \times \displaystyle (\frac {1}{R_{1}} - \frac {1}{R_{2}})|

|P| : vergence of the lense |( \delta )|
|n| : refractive index of the lense
|R_{1}| : radius of curvature of the first curved surface encountered by the light in metres |\text {(m)}|
|R_{2}| : radius of curvature of the second curved surface encountered by the light in metres |\text {(m)}|

The Optical Power of a Lense System

​|P_T=P_1+P_2+...+P_n|
|P_T| : total optical power |(\delta)|
|P_1|,|P_2|,|P_n|: individual optical power of each lense |(\delta)|
Title (level 2)
Mechanics
Title slug (identifier)
mechanics
Contenu
Corps

The Equations of Uniformly Accelerated Rectilinear Motion (UARM)

|v_{average}=\displaystyle \frac{\Delta x}{\Delta t}|

|a=\displaystyle \frac{\Delta v}{\Delta t}|

|v_{f}=v_{i} + a \cdot {\Delta t}|

|\Delta x= \displaystyle \frac{(v_{i} + v_{f}) \cdot {\Delta t}}{2}|

|\Delta x= v_{i} \cdot \Delta t +\displaystyle \frac{1}{2} \cdot a \cdot {\Delta t}^{2}|

|{v_{f}}^2={v_{i}}^2+2 \cdot a \cdot \Delta x|
|\Delta x = x_{f} - x_{i}|: displacement |\text {(m)}|
|v_{average}|: average velocity|\text {(m/s)}|
|v_{i}|: initial velocity |\text {(m/s)}|
|v_{f}|: final velocity |\text {(m/s)}|
|a|: acceleration |\text {(m/s}^2)|
|\Delta t = t_{f} - t_{i}|: time interval |\text {(s)}|

Kinematic

The Range

​|\text{Range} = \displaystyle \frac{v_i^2 \, sin\, 2 \theta _i}{g}|
|\text{Range}| : range |\text{(m)}|
|v_i| : initial velocity |\text{(m/s)}|
|\theta _i|: intinial angle from the horizontal |(^{\circ})|
|g|: gravitational acceleration |\text{(m/s}^2)|

Dynamic

Motion on an Inclined Plane

​|a = g \times \sin \theta|

 

|a|: acceleration |\text {(m/s}^2)|
|g|: gravitational acceleration |\text {(m/s}^2)|
|\theta|: angle of tilt |(^{\circ})|

Gravitational Acceleration |(g)|

​|\displaystyle g = \frac{G \cdot m}{r^{2}}|​

|g|: gravitational acceleration |\text {(m/s}^2)|
|G|: universal gravitation constant |\left(6.67 \times 10^{-11} \displaystyle \frac {\text {N} \cdot \text{m}^{2}}{\text{kg}^{2}}\right)|
|m|: mass of the celestial body |\text {(kg)}|
|r|: celestial body radius |\text {(m)}|

The Force of Friction |(F_f)|

​|F_{f} = F_{m} - F_{R}|

|F_{f}|: force of friction |\text {(N)}|
|F_{d}|: driving force |\text {(N)}|
|F_{R}|: resultant force |\text {(N)}|

|F_{f} = \mu \cdot F_{N}| |F_{f}|: force of friction |\text {(N)}|
|\mu|: coefficient of friction
|F_{N}|: normal force |\text {(N)}|

Newton's Second Law

​|F_ {R} = m \times a|

 

|F_{R}|: resultant force |\text {(N)}|
|m|: mass |\text {(kg)}|
|a|: acceleration |\text {(m/s}^2)|

The Gravitational Force |(F_g)|

​|F_{g} = m \times g|

|F_{g}|: gravitational force |\text {(N)}|
|m|: mass |\text {(kg)}|
|g|: gravitational acceleration |\text {(m/s}^2)|

|\displaystyle F_{g} = \frac{G \cdot m_{1} \cdot m_{2}}{r^{2}}| |F_{g}|: force of attraction between celestial bodies |\text {(N)}|
|G|: universal gravitation constant |\left(6.67 \times 10^{-11} \displaystyle \frac {\text {N} \cdot \text{m}^{2}}{\text{kg}^{2}}\right)|
|m_{1}|: mass of the first object |\text {(kg)}|
|m_{2}|: mass of the second object |\text {(kg)}|
|r|: distance separating the two objects |\text {(m)}|

The Centripetal Acceleration |(a_c)| and the Centripetal Force |(F_c)|

​|a_{c} = \displaystyle \frac {v^{2}}{r}|

 

|a_{c}|: centripetal acceleration |\text {(m/s}^2)|
|v|: object's rotational speed |\text {(m/s})|
|r|: radius of the circle |\text {(m)}|
|F_{c} = m \times \displaystyle \frac {v^{2}}{r}| |F_{c}|: centripetal force |\text {(N)}|
|m|: mass |\text {(kg)}|
|v|: object's rotational speed |\text {(m/s)}|
|r|: radius of the circle |\text {(m)}|

 

Transformation of Energy

Work |(W)|

​|W = F \times \Delta x|

|W|: work |\text {(J)}|
|F|: force |\text {(N)}|
|\Delta x|: displacement |\text {(m)}|

MechanicalPower |(P)|

​|P = \displaystyle \frac {W}{\Delta t}|​

|P|: mechanical power |\text {(W)}|
|W|: work |\text {(J)}|
|\Delta t|: variation in time |\text {(s)}|

Energy |(E)|

​|E_{pg} = m \times g \times \Delta y|

|E_{pg}|: gravitational potential energy |\text {(J)}|
|m|: mass |\text {(kg)}|
|g|: gravitational field intensity |\text {(m/s}^2)|
|\Delta y|: displacement (height) of the object |\text {(m)}|
|E_{pe} = \displaystyle \frac {1}{2} \times k \times \Delta x^{2}| |E_{pe}|: elastic potential energy |\text {(J)}|
|k|: restoring spring constant |\text {(N/m)}|
|\Delta x|: displacement |\text {(m)}|
|E_{k} = \displaystyle \frac {1}{2} \times m \times v^{2}| |E_{k}|: kinetic energy |\text {(J)}|
|m|: mass of the object |\text {(kg)}|
|v|: speed of the object |\text {(m/s)}|
|E_m = E_k + E_p| ​ |E_{m}|: mechanical energy |\text {(J)}|
|E_{p}|: potential energy |\text {(J)}|
|E_{k}|: kinetic energy |\text {(J)}|
 

Hooke's Law

 

​|F_{r} = - k \times \Delta x|
|F_{r}|: restoring force |\text {(N)}|
|k|: spring constant |\text {(N/m)}|
|\Delta x|: spring ellongation or compression |\text {(m)}|

The Restoring Spring Constant

In parallel:
|k_{eq} = k_1 + k_2|
In series:
|\displaystyle \frac {1}{k_{eq}} = \displaystyle \frac {1}{k_1} + \displaystyle \frac {1}{k_2}|
|k_{eq}| : equivalent restoring spring constant |\text {(N/m)}|
|k_1|,|k_2| : restoring spring constant of each spring |\text {(N/m)}|

 

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