Dot Product
multiply parallel vectors then add for SCALAR answer=56 Joules
Cross Product
use matrix to multiple perpendicular vectors to get a vector answer 3Nmi-6Nmj+3Nmk
average velocity
average velocity is the slope of the secant line
First kinematics equation (constant acceleration)
no displacment
This is also average acceleration (slope of the second line of a velocity vs time graph)
Second kinematics equation (constant acceleration)
no final velocity
most often used for projectile motion
Third kinematics equation (constant acceleration
no time
Fourth Kinematics Equation (constant acceleration)
no acceleration
Instantaneous velocity
slope of the Tangent line
Power rule forward (multiply by exponent then subtract one)
Finding Position given velocity versus time equation
Area of velocity vs time plus initial position
power rule backwards (add one and then divide by exponent) + initial condition
instantaneous acceleration
Slope of the Tangent line
power rule forwards (multiply by exponent then subtract one)
2nd derivative of position as a function of time
Final velocity from acceleration vs time equation
area of acceleration vs time plus initial condition
power rule backwards (add one then divide by exponent) + initial condition
What angle is max range off a cliff?
less than 45 degrees
Newton's Second Law, traditional
Newton's 3 Laws
Weight
depends on location and planet
Force of static Friction
static friction is a variable force!
Only as strong as it needs to be
Force of kinetic friction
depends on materials and normal force acting on object
Definition of Work (algebra)
Calculus: Definition of Work
Work for rope falling off table
if lifting rope divide by 2
Work-Energy Theorem
Defining a Potential Energy
negative work
Finding force given potential energy as a function of position
Negative Sign!
Hooke's Law
Elastic Potential Energy for Hooke's Law spring
Gravitational Potential Energy
Conservation of Mechanical energy
potential loss is kinetic gained
conservation of energy with friction
Definition of Average Power (algebra)
Definition of Instantaneous Power
energy from power
Algebra: Definition of Center of Mass
Calculus: Definition of Center of Mass
velocity of center of mass
Newton's Second Law, calculus
Impulse-Momentum
radial/ centripetal acceleration
total acceleration
no angular acceleration
linear/tangential velocity for circular motion
T is period= time for one complete circle
conversion between translational displacement and angular displacement
conversion for linear and angular velocity
tangential acceleration
angular acceleration definition (calculus)
Algebra: Definition of Moment of Inertia
Calculus: Definition of Moment of Inertia
Parallel-Axis Theorem
Rotational Inertia of disk: calculus
Rotational Inertia of rod: Calculus
Definition of Angular momentum for point particle
angular momentum for system
Definition of Torque, vector style
definition of torque (calculus)
net torque for system
Rotational Kinetic energy
Velocity when rolling without slipping
Acceleration when rolling without slipping
kinetic energy for rolling object
Kepler's 3 Laws
Universal Gravitational Potential Energy
Escape velocity
Universal Gravitational Force
Inside Planet Force due to Gravity
acceleration due to gravity
Differential Equation for SHM
Solution to Differential Equation for SHM
angular frequency for mass on spring
frequency for simple harmonic motion
Period of a mass on a spring
Period of a torsional pendulum
Period of an simple pendulum
small angle approximation
sin angle = angle
Period of a physical pendulum