Forces and Motion

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
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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
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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 - vavb/c2), where va, vb = velocity of each object & c = speed of light