# PHYS 17200 Lecture Notes - Lecture 2: 3D World

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PHYS 17200 - Modern Mechanics - Lecture 2_Momentum
Change in the 3D World
change in time = delta_t = t(final) - t(initial)
change in distance = delta_r = r(final) - r(initial)
v_avg = delta_r/delta_t
Velocity = vector = magnitude and direction
Speed = scalar = magnitude = magnitude of velocity
If we consider an interval of time t so short that interactions do not change an
object’s velocity significantly, we can compute the average velocity ~~ v_initial
Position Update formula : r_final = r_initial + v_avg*delta_t ~~ r_initial +
v_initial*delta_t
Momentum
The new measure of an object’s motion that takes its mass into account is called
its momentum (p)
For an object travelling at speeds close to the speed of light:
p = gamma*m*v ; gamma = 1 / sqrt(1-(v^2/c^2)) ; c = speed of light
For an object travelling at speeds close to the speed of light:
p =m*v because v<<c → p = 1*m*v
The perpendicular component of momentum is associated with the change in the
direction of the objects’ momentum. The parallel one with its change in
magnitude.
Newton’s Three Laws
The first law says that an object at rest tends to stay at rest, and an object in
motion tends to stay in motion, with the same direction and speed. Motion (or
lack of motion) cannot change without an unbalanced force acting.
The second law says that the acceleration of an object produced by a net (total)
applied force is directly related to the magnitude of the force, the same direction
as the force, and inversely related to the mass of the object
The third law says that for every action (force) there is an equal and opposite
reaction (force).
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