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Sep 14, 2024 · Definition of Momentum. Momentum (p) is the product of an object’s mass (m) and its velocity (v). Its formula is: p = m × v. Momentum is a vector quantity, meaning it has both magnitude and direction. The direction of momentum is the same as the direction of the object’s velocity. Everyday Examples of Momentum
momentum. Newton’s law indicates that the acceleration occurs in the same direction as the force acts. If, for an isolated system, no external force acts, then there is no acceleration. This statement is the law of conservation of momentum: that the momentum of a body is constant in the absence of a force acting on the body.
- Goals for Chapter 8
- Chapter 8: Momentum
- Restating Newton’s Second Law
- F d P
- r 'r
- Newton’s Law’s answer: When you exert a
- Momentum Conservation Answer:
- Momentum for a System is Conserved
- Types of collisions according to energy before and after the collision
- The two stick together.
- “Why do we care?”
- Visual Examples
- How do you calculate CM?
- How Does it Help?
- P m v
- CM and Problems
- Toy Rocket Problem
To determine the momentum of a particle To add time and study the relationship of impulse and momentum To see when momentum is conserved and examine the implications of conservation To use momentum as a tool to explore a variety of collisions To understand the center of mass What is momentum?
Want to deal with more complicated systems Collisions Explosions Newton’s laws still work, but using them directly gets harder: New tricks similar to energy conservation could help
“The rate of change of momentum of an object is equal to the net force applied to it” r r
dt We can check for constant mass: r r dP d(m V ) dt dt d(V ) dt m a If we exert a net force on a body, the momentum of the body changes Impulse: change in momentum
Sum of all Sum of all momentum before = momentum after True in X and Y directions separately!
force on another person, then, by Newton’s law, the person exerts an equal and opposite force on you. Everyday Experience? Cont...
Before: The system starts with zero momentum (nobody is moving) After: The system ends with zero momentum. You and your friend move in opposite directions (the one with least mass moves faster)
Momentum is ALWAYS conserved for a COMPLETE SYSTEM, you just have to look at a big enough system to see it correctly. Not conserved for a single ball in the field of gravity A ball falling is not a big enough system. You need to consider what is making it fall. Momentum is conserved if the system is closed, i.e. either “large enough” or no external...
Definitions: Elastic collision = TOTAL kinetic energy is conserved Inelastic collision = TOTAL kinetic energy is not conserved. Keep in mind Momentum is ALWAYS conserved in a collision Total Energy may or may not. Q: where does the energy go?
What is their speed after the collision? Show that this is inelastic
• This is a special point in space where “it’s as if the object could be replaced by all the mass at that one little point” Center of Mass (CM) Cont... Examples where this is useful: We can model the earth moving around the sun as a single point at “the center of the earth” There is only one point on a stick that you can put your finger under and h...
The center of mass has the same trajectory in both cases since both have the same acceleration and initial velocity
Pick an origin Look at each “piece of mass” and figure out how much mass it has and how far it is (vector displacement) from the origin. Take mass times position Add them all up and divide out by the sum of the masses The center of mass is a displacement vector “relative to some origin”
• Remember equation for momentum of a system of objects?
' ' m v i i Now I can re-write it as: d x P m v m d(m x ) d(m x / i M i M ) i dt i i dt dt i d(m M / M ) d d M ( m x / M ) ) M X dt dt i M VCM CM i dt I can write one equation for multi-component system and treat it as a single object, where e.g. momentum is perfectly conserved Think of describing Solar system mo...
Solving collision/explosion problems: Conservation of Momentum in all directions Watching the Center of Mass Need to be able to do both – Pick easier method
Your friend fires a toy rocket into the air with an unknown velocity. You observe that at the peak of its trajectory it has traveled a distance d in the x-direction and that it breaks into two equal mass pieces. Part I falls straight down with no initial velocity. Where does the 2nd half of the toy end up?
Jul 28, 2023 · Momentum is a fundamental property in physics and is defined as the product of the object’s mass and velocity. It is a vector quantity having both magnitude and direction. A car moving on a road has momentum. A soccer ball gathers momentum when it is kicked. Formula. Since momentum is the product of mass and velocity, it is given by.
History. Past Papers. Religious Studies. Revision notes on Momentum & Impulse for the Cambridge O Level Physics syllabus, written by the Physics experts at Save My Exams.
1. Physical Chemistry. Lecture 15 Angular Momentum and the Rigid Rotor. Angular momentum. Vector property that describes circular motion of a particle or a system of particles Rigid rotor model: A particle of mass m fixed to a massless rod Examples. Swinging a bucket of water. Movement of the Earth around the Sun. L 2.5 x 1040kg m2s-1 L r p.
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Jul 16, 2024 · Generally, momentum implies a tendency to continue on course—to move in the same direction—and is associated with great mass and speed. Momentum is important because it is conserved. Only a few physical quantities are conserved in nature, and studying them yields fundamental insight into how nature works, as we shall see in our study of ...
