Forces and Motion

• see also:
  • work, energy & power

Some basics:

• average speed = distance travelled / time elapsed
• velocity is a direction and speed vector
• instantaneous velocity is the gradient of a distance vs time graph of the object's motion
• average acceleration = change in velocity / time elapsed
• instantaneous acceleration is the gradient of a velocity vs time graph of the object's motion
• relative velocity between two objects is the vector subtraction of the two velocities (see also Einstein)
• terminal velocity is the vertical velocity of a falling object at which the force of air resistance is just sufficient to balance the gravitational force on its mass
  • acceleration of a free falling body at sea level and 45deg latitude = 9.80 m/sec²
  •  

Newtonian laws of motion of objects:

• three laws of motion:
  • the law of inertia:
    • a body remains at rest or continues to move with constant velocity unless acted upon by a net force
  • the law of force and acceleration:
    • a force is needed to change the velocity of an object, that is to accelerate it. When a net force Fn does act on an object, it produces an acceleration a in the direction of the force, given by:
      • net force = mass of object x acceleration
        • force in newton, mass in kg, acceleration in m/sec²
        • nb. force is the area under a acceleration vs time curve
      • at any given instant, the instantaneous net force produces an instantaneous acceleration as above.
  • the law of reacting forces:
    • to any force which acts on a body, there is always an equal and opposite reaction force acting on another body thus momentum is conserved in any collision process
    • ie. if there is no external force acting on a system of bodies, the momentum of the system does not change
      • momentum = mass x velocity
      • eg. momentum of recoil of gun = - momentum of bullet
      • impulse = change in momentum = force x time elapsed
• the law of universal gravitation:
  • every particle in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the two particles & inversely proportional to the square of the distance between the centres of mass
    • force of gravity = Gm₁m₂/s
      • G = gravitational constant = 6.67 x 10-11 newton-m2/kg2
      • s = distance between centres of mass of two objects in metres
      • m₁m₂ are the respective masses of each object in kg
•  

Einstein's theory of relativity:

• sorry can't go faster than speed of light as you get heavier & need exponentially more energy to go faster:
  • mass = mass at rest / sqrt (1 - v²/c²), where v = speed & c = speed of light
• relative velocity of two objects:
  • relative velocity _AB = (va - vb) / sqrt (1 - v_av_b/c²), where v_a, v_b = velocity of each object & c = speed of light