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2011-11-25 01:20:20
Equations Definitions Mechanics

The equations and definitions concerning Newton's laws of motion and momentum
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  1. Newton's First Law of Motion States:
    If there is no resultant force acting on an object:

    - If it is at rest, it will remain at rest

    - If it is moving, it will keep on moving at a constant velocity
  2. Newton's Second Law of Motion States:
    The rate of change of momentum of an object is directly proportional to the resulting force acting on it

    The change in momentum takes place in the direction of that force
  3. Newton's Third Law of Motion States:
    If object A exerts a force on Object B; Object B will exert an equal yet opposite force on A

    • Put Simply:
    • To every action there is an equal but opposite reaction
  4. How can Newton's Second Law be expressed?
    Resultant force = Change in Momentum / Time Taken

    F = (mv - mu) / t

    So if the mass is constant it will become

    F = m x (v - u) / t

    which equals

    F = ma
  5. Momentum

    What is the equation for Momentum?

    What is Momentum measured in?
    Momentum (p) = Mass (m) x Velocity (v)

    Kilogram per Meter per Seconds - Kg m s-1
  6. What is the definition of 1 Newton (1N)
    1 Newton is the resultant force needed to give a mass of 1Kg an acceleration of 1 ms-2
  7. Change in Momentum and Impulse

    1) What is the equation of change in momentum?

    2) Where does this equation come from?

    3) What is impulse?

    4) What is the equation for impulse?
    1) kgms-1 = Forec (N) x Time (s)

    2) Rearranging Newton's 2nd Law equation:

    Resultant Force = Change in Momentum/ Time

    3) Impulse is the measure of the effect of a force and is measured in Newtons per second (Ns)

    4) Impulse (Ns) = Change in Momentum kgms-1

    = Force (N) x Time (s)
  8. Force - Time Graphs

    The area under a Force - time graphs represents....
    The total impulse acting =

    total change in momentum produced
  9. Conservation of Momentum

    The equation for the Conservation of Momentum is:
    • Total momentum before impact
    • =
    • Total momentum after impact
  10. Displacement- Time Graphs

    What do they show?
    The gradient of the curve = Velocity
  11. Velocity - Time Graphs

    What do they show?
    Gradient of the curve = Acceleration

    Area under the curve = Displacement
  12. What are the four equations of motion?
    1) v = u + at

    2) s = 1/2 (v + u) t

    3) s = ut + 1/2at2

    4) v2 = u2 + 2as
  13. Work/ Energy

    What is the equation for Work Done (Energy)?
  14. Work Done (J) = Force (N) x Displacement (m)
  15. What is 1 Joule?
    1 Joule is the work done (or energy) when a force of 1N moves through a distance of 1m
  16. Power

    What is the equation for power?

    What is the alternative equation for power?
    Power (W) = Work Done (J) / Time Taken (s)

    Power (W) = Force (N) x Average Velocity (ms-1)
  17. Kinetic Energy

    What is the equation for Kinetic Energy (Ek)?
    • Ek = 1/2 x m x v2
    • = 1/2 x mass x velocity squared
  18. Potential Energy

    What is the equation for the change in Gravitation potential energy (ΔEp)?
    ΔEp = mgΔh

    Mass x gravitational field strength x difference in height
  19. Collisions

    What are the two type of collisions?

    What happens to the kinetic energy in these collisions?

    What is the Ek equation for this collisions?
    1) Elastic collision

    Kinetic energy is conserved

    Total Kinetic before collision = Total after collision

    2) Inelastic Collision

    % of Kinetic energy is transferred to other forms

    Total K energy before collision is greater than total K energy after collision
  20. Radians

    What is the equation to find the number of radians in an angle?
  21. θ in radians = length of arc / radius
  22. Angular Speed

    What is angular speed?

    What is it's equation?
    Angular speed is the θ turned through in a given time

    Angular Speed (w) = Angle θ / Time taken


    w = 2πf
  23. Centripetal Acceleration

    What is the equation for centripetal Acceleration?
    a = v2 / r


    a = rw2
  24. Centripetal Force

    What is the equation for centripetal Force?
    F = mv2 / r


    F = mrw2