General Physics - Lesson 1 2Q: Center of Mass, Momentum, Impulse, and Collisions

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