MCAT Kaplan Physics and Math Chapter 1: Kinematics and Dynamics

metric system

System of units that can be in MKS (meters kilogram seconds) or CGS (cm, grams, seconds). MKS system is know as SI units.

SI units

Base units include:

length: m

mass: kg

time: s

current: A

Amount: mol

Temp: K

Luminous intensity: cd (candela)

Derived Units for SI units

Force: N (kg x m/s^2)

work and energy: J (kg x m^2/s^2)

Power: W (kg x m^2/s^3)

Derived Units for CGS

Force: dyne (g*cm/s^2)

work and energy: erg (g*cm^2/s^2)

Power: erg/s

nm

1x10^-9 m

Angstroms

10^-10 m

electron volts

-alternate unit for work/energy

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

-1eV = 1.6E-19 J

Vectors

quantities that have both a magnitude and a direction

Scalars

quantities, such as temperature or distance, that are just numbers without any direction

resultant vector

the vector sum of 2 or more vectors or the vector resulting from a cross product (ex: V is a _____ of V=AxB)

Tip to tail method

a method for finding a resultant vector in vector addition, in which the tail of one vector is drawn from the tip of another vector

components of vectors

vectors can be split into _________ using the rules shown in the image. __________ can be added directly into components of resultant

Pythagorean Theorem for vectors

By summing up the squares of vector components and taking the square root, one can get the magnitude of the vector itself.

Finding the angle of resultant vector.

vector subtraction

To subtract two vector graphically, reverse direction of subtracted vector then do vector addition. May be performed on components of vectors first.

Multiplying Vectors by Scalars

When ________, the vector magnitude is scaled by scalar, the resultant vector direction will be parallel to original vector if scalar is positive and antiparallel to the original if scalar is negative. Note that units multiply as well.

dot product

When vector multiplied with another vector yields a scalar quantity

formula is |a| x |b| x cos(angle)

cross products

multiplication of two vectors to give a third vector with magnitude and direction. Direction determined by right-hand rule. Resultant will always be perpendicular to both vectors. Note that units multiply as well.

displacement (x)

Distance and direction of an object's change in position from the starting point. Vector quantity. Does not take into account path traveled

distance traveled

The length of a path between two points. Scalar quantity.

velocity (v)

vector quantity with magnitude measured as rate of change of displacement in a given unit of time. m/s. Direction of velocity is same as direction of displacement

speed (v)

The distance an object travels per unit of time. A scalar quantity

instantaneous speed

equal to the magnitude of instantaneous velocity

instantaneous velocity

the velocity of an object at some instant or at a specific point in the object's path

average speed

total distance traveled divided by total time. Accounts for path traveled, unlike average velocity.

average velocity

the total displacement divided by the time interval during which the displacement occurred. Does not account for path traveled.

force (N)

vector quantity experienced as pushing or pulling on objects

gravity

A force of attraction between objects that is due to their masses. G is universal gravitational constant (6.67 x10^-11 N*m^2/kg^2)

Friction

A force that opposes motion between two surfaces that are in contact

static friction (f_s)

friction that exists between stationary object and the surface upon which it rests

static friction inequality

Shown in image. mu_s is coefficient of static friction (unitless and dependent on two materials in contact), N is normal force.

Value of static friction equal to that of force applied. At static friction of 0, no force is applied. If force applied is greater than mu_s*N, then object begins to move.

kinetic friction (f_k)

friction between a sliding object and the surface over which it slides. (note that a wheel moving does not involve kinetic friction)

kinetic friction equation

f(k)= u(k)N

where f(k)=kinetic friction

u(k)=coefficient of kinetic friction

N= magnitude of the normal force

Has constant value, does not depend on surface area in contact or velocity of sliding object. Kinetic friction coefficient is always smaller than the static friction coefficient, showing that it is easier to keep object moving than to start it moving.

mass (m)

Measure of a body's inertia. Scalar, does not depend on gravity

weight (F_g)

Measure of gravitational force on an object. F=mg. Unit of N

weight-mass equation

g is approx 10 m/s^2

center of mass

the point in an object that moves as if all the object's mass were concentrated at that point. Geometric center of an object that is symmetrical in shape and uniform in density. Can be calculated with equation shown, but not required to know this for the MCAT

Acceleration

rate of change of velocity

average acceleration

the change in velocity during some measurable time interval divided by that time interval

instantaneous acceleration

On a graph of v vs. t, slope of tangent line at a given t.

Newton's First Law

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Also called law of inertia.

Newton's Second Law

An object's acceleration depends on its mass and on the net force acting on it.

Newton's Third Law

For every action there is an equal and opposite reaction

linear motion

When the object's velocity and acceleration are along the line of motion, so the pathway of the moving object continues along a straight line

kinematics equations

free fall

the motion of a falling object when the only force acting on it is gravity (i.e. no air resistance)

air resistance

Fluid friction acting on an object moving through the air. Value increases with speed of the object

drag force

a force that opposes the motion of an object through a fluid

terminal velocity

the constant velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity

projectile motion

the curved path that an object follows when thrown, launched, or otherwise projected near the surface of Earth. v_x usually remains constant

inclined plane

a slanted surface along which a force moves an object to a different elevation

split gravity into Fg_parallel to plane=mgsin(theta), Fg_ perpendicular to plane=mgcos(theta)

circular motion

occurs when forces cause an object to move in a circular pathway

uniform circular motion

the movement of an object at a constant speed around a circle with a fixed radius. Velocity vector always tangent to path, centripetal force points radially inward. Centripetal force generate centripetal acceleration. Tangential force is always zero because speed does not change

Centripetal force is F_c=m x V^2/r

centripetal force in uniform circular motion

r is the radius of circular path, v is velocity, m is mass

dynamics

the study of forces and torques

free body diagram

a diagram showing all the forces acting on an object

translational motion

objects moving without rotating

Translational Equilibrium

net force acting on a body is zero, also known as first condition of equilibrium. Object will have a constant speed and acceleration.

fulcrum

the pivot point of a lever

Torque (moment of force)

turning effect produced by a force

Torque is cross product of F and moment arm.

lever arm

distance between the applied force and the fulcrum

Torque equation

Torque is the cross product of force and moment arm (tau= r x F)

F is magnitude of fore, r is the length of the lever arm, theta is angle between the lever arm and the force vectors

rotational equilibrium

occurs when an object's net torque is zero. On MCAT, means object is not rotating