Momentum = mass x velocity OR p = mv
MOMENTUM IS ALWAYS CONSERVED (assuming no external forces act)
- This means total momentum before = total momentum after
- Can be applied to explosions and collsions
- Remember than negative symbols (-) are used to show the direction of the motion.
When working in two dimensions use resolve vectors to solve momentum problems:
- Draw a labelled diagram from the information given in the question.
- Use SOH CAH TOA to resolve the vector into it's vertical (y) and horizontal (x) components.
- Both components will be conserved dueing the collsion.
- Only the component parallel to the line of collision will have any affect - the line of collision is the line where the centre of object A meets the centre of object B.
- The component of velocity that is perpendicular to the line of collsion will have no effect.
Force and Energy
- "The rate of change of momentum of an object is directly proportional to the resultant force which acts upon it." - This can be derived from newtons second law.
This translates to F = Δmv / Δt
When mass is constant, this gives F = ma
- "Energy cannot be created or destroyed, only tranferred from one form to another, but the total amount of energy in a closed system will not change"
Kinetic energy: Ek = 1/2mv² You can get another equation momentum:
- p = mv - substitute pinto Ek = 1/2mv²
- Ek = pv/2
- from p = mv we can rearrange to get v = p/m - substitute into equation
- so: Ek = p²/2m
Kinetic energy may not always be conserved. If a collsion is ELASTIC, KE is CONSERVED. If a collision is INELASTIC, KE is NOT CONSERVED
When talking about circular motion, you may need to use RADIANS to express angles. The angle in radians is defined as arc length divided by the radius of the circle. To convert from degrees to radians: angle in radians (θ) = (2pi/360) x angle in degrees
The ANGULAR SPEED is the angle an object rotates through per second: ω = θ/t
you can link linear speed (distance/time) with angular speed: v=ωr
Circular motion has a frequency and period: ω = 2πf and T = 2π / ω
Objects travelling in circles are acclerating because their veolcity is constantly changing (because their direction is constantly changing.) This is called CENTRIPETAL ACCELERATION - it is always directed towards the center of the circle. It can be calculated using these equations: b a = v² / r and a = rω²
By Newtons Second Law, acceleration must be cause by a force. Centripetal acceleration must be caused by a CENTRIPETAL FORCE this is not an extra force - it is just used to describe the force is F = mv²/r a = rω² causing the centripetal acceleration - it could be tension etc.