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Center of Mass
A point where the mass of the system is concentrated (Example: Ice Skater balancing on a point of support)
Geometric Center
Physical Center of a system where x and y coordinates intersect, (Center of the body) the point that sets the origin and locations
Factors that account for Center of Mass
Mass of System and Location of objects in an arbitrary coordinate system
Geometric Shapes with Uniform Composition
Cylinder, Pyramid, Sphere, Cube, Rectangle
Formula for Center of Mass of bodies for X and Y (xc and yc)
xc = m1x1 + m2x2 +m3x3+.../m1+m2+m3+...
yc = m1y1 + m2y2 +m3y3+.../m1+m2+m3+...
where m is mass x is points in x axis y is points in y axis
Formula for Center of Mass
m = (xc, yc)
where xc is the center of mass in x direction
where yc is the center of mass in y direction
Momentum
Product of mass m of the object and its velocity v
Formula for Momentum
P (momentum) = mv
where p = kg m/s where m = kg where v = m/s
Higher Mass (Center of Mass)
Closer to center of mass
Lower Mass (Center of Mass)
Farther to center of mass
2 Important Components of Momentum
How much is moving (mass) and How fast is it moving (velocity)
Impulse
Product of the net force acting on the object and the time interval of the net force's action, when you apply force to an object at a specific time
Momentum and Impulse Quantities
Vector Quantities since they have direction
Formula for Impulse
I = F [triangle] t
Where I is the impulse Where F with the triangle is the average force Where t is the time
Relationship of Force and Time
Inverse relationship in impulse, when one increases the other decreases
(example: great force in little time and little force over a long period of time)
Impact Momentum Theorem
The change in momentum of an object during a particular time interval is equal to the impulse of the net force that acts during the time interval
Where I = [triangle] p meaning impulse equal to total momentum
Where F [triangle] t = mvf - mvi meaning constant mass with initial and final velocity
Conservation of Momentum
In an isolated system where the net external force is zero, the total momentum of the system is constant, The final and initial states are equal
Formula for Conservation of Momentum
Initial Momentum = Final Momentum
wherein
m1v1i + m2v2i = m1v1f = m2v2f
where m = mass v = velocity i = initial f = final
Formula for Conservation of Kinetic Energy
Initial Kinetic Energy = Final Kinetic Energy
wherein
[(1/2)m1v1i + (1/2)m2v2i] = [(1/2)m1v1f + (1/2)m2v2f]
Elastic Collision
Has conserved Momentum and KE and does not stick together
Inelastic Collision
Has conserved Momentum and does not conserve KE and either does not stick or partly sticks
Perfectly Inelastc
Has conserved Momentum and does not conserve KE and completely sticks
