Kinematics and Dynamics Flashcards by Sayan Basu

British/Imperial System (FPS)

Foot, Pound, Second

rarely used by MCAT

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Metric Systm (MKS)

Length -> Meter
Mass -> Kilogram
Time -> Second
Current -> Ampere
Mole -> Mol
Temperature -> Kelvin
Luminous Intensity -> Candela

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Base vs Derived Units

B: standard units a system is designed around (seconds, kgs)

D: base units associated together (newton, joule, watt) for force, energy and power)

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Angstroms

1 A = 10^-10 m

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Electron volt

energy gained by an electron accelerating through a 1 V potential difference

1eV = 1.6*10^-19

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Vectors (Bold)

numbers with magnitude and direction (displacement, velocity, acceleration, force)

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Scalars (italic)

numbers only with magnitude

distance, speed, energy, mass, pressure

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Resultant

sum or difference of two or more vectors

sum of A and B is to place tail of B at tip of A, the sum will be tail of A to the tip of B

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Right Traingle for Vectors

V = Hyp
X and Y

X = Vcos theta
Y = V sin theta

V = X^2 + Y^2

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Angle of Resultant Vector

theta = tan^-1 (Y/X)

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Steps to Finding Results via Components

1) Resolve vectors into X and Y components
2) add all x components for Rx ; add all y components for Ry
3) Magnitude of resultant is sqrt(Rx^2 + Ry^2)
4) Direction is theta= tan-1 (Ry/Rx)

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Vector Subtraction

like addition but subtract all x components from each toher and all y components from each other

A - B = A + (-B)

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Multiplying Vectors by scalars

R = (n) A where n = scalar

magnitude is A* abs(n)
direction depends on sign where negative n is opposite directions and positive n is same direction

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If vector A is multiplied by scalar -3, then new Vector B is…

three times as long as A and in opposite directions

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Multiplying 2 Vectors: Dot Product

develops scalar quantity like work (F * D)

A * B = (A)(B) cos (theta)

where ( ) is the resultant value of the vectors ex: sqrt (Ax^2 + Ay^2)

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Multiplying 2 Vectors: Cross Product

when generating a third vector and needing its magnitude and direction like torque

A x B = (A) (B) sin (theta)

where ( ) is the resultant value of the vectors ex: sqrt (Ax^2 + Ay^2)

**use right hand rule to determine the direction!

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The resultant of a cross product will always be ____ to the plane created by the two vectors

perpendicular

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Displacement (x)

an object in motion may experience a change in its position in space.

Vector quantity, ONLY NET CHANGE DOESNT CONSIDER PATH

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Distance (d)

considers path taken and is a scalar quantity compared to displacement

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Velocity (v)

vector and is the rate of change of displacement in given time

(m/s)

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Speed

distance traveled in a given time

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Instantaneous Speed vs Instantaneous Velocity

IS is equal to the magnitude of IV

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Instantaneous Velocity

V = lim as t -> 0 of dx/dt

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Average Velocity

V = delta x / delta t

where delta x is change in position

Average Speed

v = d/t

Force

vector quantity causing a pushing or pulling between two objects that are not necessarily touching Newtons

Gravity

attractive force felt by all forms of matter all objects exert a gravitational force on each other

Magnitude of Gravitational Force

F = ( Gm1m2 )/ (r^2) r is distance between the two center of massses

Friction

force that opposes the movement of objects two types: statc and kinetic

Static Friction (fs)

between a stationary object and surface 0 < fs < usN ranges between 0 and the max force generated from static friction coefficient and normal force

Coefficient of Static Friction

unitless quantity dependant on the two materials in contact

Kinetic Friction (fk)

SLIDING object and material it slides over fk = ukN always constant value! smaller than us

Difference between us and uk

uK is always smaller than uS and is constant

Mass (m)

amount of matter in the object, body's inertia scalar and independent of gravity

Weight (Fg)

measure of gravitational force on a objects mass Newtons Fg = m*g

Only for a ____ body with ___ shape and uniform density can the center of gravity be located in the _____

homegenous symetrical, center

Acceleration (a)

rate of change of velocity an object experiences as a result of some applied force vector quantty a = dV/dt

Instantaneous Acceleration

a = lim as t -> 0 of dV/dT

Tangent line of V vs T graph is....is positiv slope...if negative slope....

acceleration aceeleration is positive and in direction of velocity acceleration is negative and against velocity

Newtons First Law

F = ma = 0 Law of Inertia body either at rest or in motion with constant velocity will remain as such unless a net force acts on it.

Newtons Second Law

F=ma An object of mass m will accelerate when vector sum of the forces results in some nonzero resultant force vector

Newtons Third Law

Fab == - Fab To every action there is an opposed but equal reaction no physical contact is necessary

Linear Motion

objects velocity and acceleration are along the line of motion so object continues in a straight line not just vertical or horizontal

One Dimensional Equations

v = vo + at x =Vot + (at^2)/2 V^2 = vo^2 + 2ax x = Vt ``` z = displacement V = average velocity ```

During free fall problems, the velocity when ball is at its maximum height is ___

Air resistance increases as the speed of an object _____ , the object ten experiences _______ as the magnitude of velocity increases. Eventually, this will be equal in magnitude to the weight of the object and object will fall with constant velocity according to newtons 1st law known as _______

increases, drag force, terminal velocity

Projectile Motion

follows a path along 2 dimensions with velocities and accelerations in two directions that are independent of one another vy changes at rate gravity but vx will remain constant!!

Inclined Planes

motion in two directions Fgx = mgsin(theta) Fgy = mgcos(theta)

Circular Motion

force causes object to move in circular pathway, displacement in one loop is 0

Uniform Circular Motion

instantaneous velocity vector is tangent to circular path, meaning inertia makes it want to escape in a tangent path

Centripetal Force

force radially inward which prevents object from escaping uniform circular motion Fc =( mv^2 )/ r

In uniform circular motion, the tangential force is _____ because there is no change in the ___ of the object

0 , speed

Centripetal acceleration

generated by the centripetal force

Translational Motion

force causes an object to move without any rotation, usually linear

Translational Equilibirum

vector sum of all the forces acting on an object is equal to zero, similar to Newtons first law object will have constant velocity: a constant speed (0 or non zero value) and a constant direction

Rotational Motion

when forces applied against an object cause object to rotate around a pivot point known as fulcrium

Torque

moment of force r x F = rF sin (theta) r = length of lever arm

Rotational Equilibrium

vector sum of all torques is equal to 0 clockwise = negative counterclockwise = positive