Dynamics

Inertia, mass, acceleration

$$\frac{a_1}{a_2} = \frac{m_2}{m_1}$$

m1, m2 - masses of interacting bodies
a1, a2 - accelerations

Find It is known that:

Calculate 'a1'

Force, mass, acceleration

$$F = m\cdot a$$

F - force
m - mass
a - acceleration

Find It is known that:

Calculate 'F'

Gravity force

$$N = m\cdot g$$

N - gravity force
m - mass
g - free fall acceleration

Find It is known that:

Calculate 'N'

Friction force

$$F_{tr} = \mu\cdot N$$

F_fr - friction force
μ - coefficient of friction
N - gravity force

Find It is known that:

Calculate 'F_fr'

Friction force

$$F_{tr} = \mu\cdot m\cdot g$$

F_fr - friction force
μ - coefficient of friction
m - mass
g - free fall acceleration

Find It is known that:

Calculate 'F_fr'

Law of universal gravitation

$$F = \frac{G\cdot (m_1\cdot m_2)}{r^{2}}$$

F - force
G - gravitation constant
m1, m2 - masses of interacting bodies
r - distance

Find It is known that:

Calculate 'F'

Centripetal acceleration of satellite

$$a = \frac{v^{2}}{R+h}$$

a - acceleration
v - speed (velocity)
R - radius of the Earth
h - height

Find It is known that:

Calculate 'a'

Speed (velocity) of satellite

$$v = \sqrt {\frac{G\cdot M}{R+h}}$$

v - speed (velocity)
G - gravitation constant
M - Earth mass
R - radius of the Earth
h - height

Find It is known that:

Calculate 'v'

First cosmic velocity (move in a circular orbit)

$$v = \sqrt {g\cdot R}$$

v - speed (velocity)
g - free fall acceleration
R - radius of the Earth

Find It is known that:

Calculate 'v'

Second (escape) cosmic velocity (overcome gravity)

$$v = \sqrt {2\cdot g\cdot R}$$

v - speed (velocity)
g - free fall acceleration
R - radius of the Earth

Find It is known that:

Calculate 'v'

Kepler's Third Law

$$\frac{T_1^{2}}{T_2^{2}} = \frac{a_1^{3}}{a_2^{3}}$$

T1, T2 - orbital periods of planets
a1, a2 - semi-major axis (semiaxis) of the orbit

Find It is known that:

Calculate 'T1'

Free fall acceleration at the earth's surface

$$g = \frac{G\cdot M}{R^{2}}$$

g - free fall acceleration
G - gravitation constant
M - Earth mass
R - radius of the Earth

Find It is known that:

Calculate 'g'

Body weight

$$P = m\cdot g$$

P - weight
m - mass
g - free fall acceleration

Find It is known that:

Calculate 'P'

Body weight: weightlessness

$$P = m\cdot (g-a)$$

P - weight
m - mass
g - free fall acceleration
a - acceleration

Find It is known that:

Calculate 'P'

Body weight: overload

$$P = m\cdot (g+a)$$

P - weight
m - mass
g - free fall acceleration
a - acceleration

Find It is known that:

Calculate 'P'

Braking (stopping) time

$$t = \frac{m\cdot v}{F_{tr}}$$

t - time
m - mass
v - speed (velocity)
F_fr - friction force

Find It is known that:

Calculate 't'

Braking (stopping) time

$$t = \frac{v}{\mu}\cdot g$$

t - time
v - speed (velocity)
μ - coefficient of friction
g - free fall acceleration

Find It is known that:

Calculate 't'

Braking (stopping) distance

$$s = \frac{m\cdot v^{2}}{2\cdot F_{tr}}$$

s - path (distance)
m - mass
v - speed (velocity)
F_fr - friction force

Find It is known that:

Calculate 's'

Braking (stopping) distance

$$s = \frac{v^{2}}{2\cdot \mu\cdot g}$$

s - path (distance)
v - speed (velocity)
μ - coefficient of friction
g - free fall acceleration

Find It is known that:

Calculate 's'

Rolling friction force

$$F_{tr} = \frac{\mu\cdot N}{R}$$

F_fr - rolling friction force
μ - rolling resistance coefficient
N - gravity force
R - radius

Find It is known that:

Calculate 'F_fr'

Elastic force

$$F_{tampr} = k\cdot x$$

F_elast - elastic force
k - stiffness
x - elongation (shortening) of the object

Find It is known that:

Calculate 'F_elast'

Kinetic energy or rotating body

$$W_{k} = \frac{J\cdot \omega^{2}}{2}$$

W_k - kinetic energy
J - inertia moment
ω - angular speed (velocity)

Find It is known that:

Calculate 'W_k'