12 Mar 2015

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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).