Calculate force from mass and acceleration
Calculate gravitational force between objects
Calculate how far something will travel
Convert between different units quickly
Calculate energy of moving objects
Calculate energy due to height
Force needed for circular motion
Calculate work from force and distance
1 N = 0.225 lbf
1 kg = 2.205 lb
1 m = 3.281 ft
1 J = 0.239 cal
g = 9.81 m/s² (Earth gravity)
G = 6.67×10⁻¹¹ N⋅m²/kg²
c = 3×10⁸ m/s (speed of light)
Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Mathematical Expression:
If ΣF = 0, then dv/dt = 0
Therefore: v = v₀ (constant velocity)
The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
Principle of Action and Reaction:
|F₁₂| = |F₂₁|
F₁₂ + F₂₁ = 0
Every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Interactive simulation demonstrating Newton's laws of motion in action. Observe how forces affect the motion of objects according to the principles established in the Principia.
Calculate orbital parameters using Newton's derivation of Kepler's laws. These calculations demonstrate how the Principia unified celestial and terrestrial mechanics.
Analysis of projectile motion under gravity, demonstrating the separation of horizontal and vertical components of motion as described in the Principia.
Physical parameters of celestial bodies as used in gravitational calculations. These values enable precise orbital mechanics computations.
Where:
F = centripetal force
m = mass of the object
v = velocity
r = radius of circular path
Newton's derivation of Kepler's Third Law:
T = orbital period
M = mass of central body
r = semi-major axis
G = gravitational constant
dp/dt = F
If F = 0, then p = constant
Work-energy principle:
W = ∫F·ds = ΔKE
Proposition: The gravitational force between two masses is inversely proportional to the square of their distance.
Proof:
1. Consider a sphere of radius r with mass M at its center
2. The gravitational flux through the sphere is proportional to M
3. The surface area of the sphere is 4πr²
4. Therefore, gravitational field strength ∝ M/(4πr²)
5. Force on test mass m: F = GMm/r²
Proposition: For uniform circular motion, a = v²/r
Proof:
1. Consider velocity change Δv over small time Δt
2. For circular motion: |Δv| = v × (vΔt/r)
3. Acceleration: a = |Δv|/Δt = v²/r
4. Direction is toward center (centripetal)