Map of Mechanics (Physics)

Kinematics

Forces

Work/Energy

Momentum

Rotational Dynamics

Circular Forces

Centripetal Force

Centrifugal (false/fake/non-existant)

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Ciruclar Accelerations

tangential acceleration

radial acceleration

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Friction

Kinetic

Static

Rolling

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just the apparent force you feel, there isn't actually a force, just inertia of the rotation redirecting your velocity under the radial acceleration.

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Fluid Resistance

For slow Speeds in a fluid, the friction on the object is

at higher speeds, the friction becomes proportional to the square of velocity, so the friction becomes

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Terminal Speeds

For slow moving objects, the terminal speed is (when Fg = fluid resistance; when mg = kv)

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For quicker objects, mg = Dv^2

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Kinematic Formulas

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acceleration

velocity

distance

initial distance + definite integral of velocity over the interval

initial velocity + definite integral of acceleration over the interval

instantaneous

is the limit as time -> 0

average

is the change in acceleration/velocity/distance over the change in time.

For a,v,or x

Used in problem solving for values - look for the missing variable to find the right formula

Collisions

Impulse

p=mv - p and v are vectors

J = Net force x change in time

J = change in momentum

J = definite integral of net force over time

usually very short times, in milliseconds, with massive net force.

collision classes

Some elasticity

Completely Inelastic

Completely Elastic

Bodies will have the same final velocity

Some kinetic energy lost

kinetic energy is conserved

momentum is conserved

conservation of kinetic energy in elastic collision:

NOTE: the kinetic energy is not a vector! so the x/y components are not conserved, the overall energies of the intial movement and the final movement is conserved!

momentum is conserved

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Lost Energy in Collisions:

Lost kinetic energy = initial KE - final KE

KE = 1/2m(p/m)^2

since momentum/mass = speed

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the same is true for y values

NOTE: the momentum is conserved only in the components of the vectors, since momentum in non-scalar, you can have two bodies seemingly gain momentum in the y-direction, but its actually just the conservation of momentum working properly.

Center of Mass

the center of mass for a collection of masses is the sum of the bodies respective position times mass, over the sum of the masses

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CM is the mass-weighted position of particles

a spinning object, like a tennis racket, will spin around its CM, with the CM following the projectile trajectory

when an object breaks apart in a projectile motion system, the cm will follow the original course, but the split objects will diverge

Total mass x velocity of center of mass = total momentum #

net external force = total mass x acceleration of cm #

Newtons Laws

net force = 0; acceleration = 0

Fa on b = -Fb on a

net force = mass x acceleration

Projectile Motion

Projectile Motion Equations

[on paper]

Coordinates

Velocities

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Accelerations

ax = const, 0

ay = g

Work

Energy

Kinetic

Potential

W = Scalar product: F * s

W = Fs (force x displacement)

W = Fscos(theta)

K = 1/2mv^2

Work - Energy Theorem:

Wtot = K2 - K1 = deltaK

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Negative Work

ex: pushing against the direction of motion for a moving object

Variable Work

Integral of the Force function over a definite distance

Springs

Fx = -Kx

the restoration force, has the neg because its opposite its direction of pull, the applied force.

Power

P = W/t

P = dot product: F*v (force times dot product velocity)

Conservation of Energy

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normal

tension

gravitational

rotating bodies / tangential x, v, and a

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Rotational dynamics equations (basically the kinematics but rotating with angles

energy

inertia

parallel axis theorem

kinetic

KE = 1/2 x I x w^2 (half times moment of inertia at pivot point times angular velocity squared)

Ip = Icm + md^2

parallel axis theorem #

Ip = Icm x md^2