Lecture 2 | Modern Physics: Classical Mechanics
Aristotle 's law is a consistent mathematical law. Aristotle thought that in order to keep an
object moving you had to exert a force on it. an object moving through free space under its own
inertia will keep moving without an external force. in order to follow the system. All you need to
know is at the end at the initial starting point. the force only changes because the particle
moves and depending on where the particle is the force will change. the derivative of the force
with respect to position tells you how much the force changes when you move from one
position to another times how fast you move the x-Dt. In fact, if you look at this equation, you 'll
notice it 's correct because you can cancel out the dx. The f dt is the f by the x-dx by dt. if we
know. F of X? We also know DF by dx and the first equation up. Here tells us what the velocity is.
the op shot is. In fact we do know the jerk we a moment ago convinced ourselves that if we
know the initial position, we also know about the velocity in the acceleration. Well all that goes
in here is velocity and acceleration and knowledge of the force law. you can build up the entire
motion. If all you know is the at one instant of time. Now as I said this is a false law..
The lesson is in Newton 's equations, which are Secondorder equations which in all second
derivatives with respect to time, you need to know to get started positions and velocities. the
force law might depend not only on the position of particles, but it might depend on the different
other position relative positions and so forth.. If you know all the positions of all particles, then it
's assumed that you know the force on every single one of them due to all the others that's the
assumption of Newton. a force law like this is again unphysical. It never occurs in nature. the
components of force in a given direction are proportional to how fast the potential energy is
changing along that direction.. we 'll generalize this to many particles. In fact, we 'll. generalize it
to arbitrary systems, but let 's take the case of a single particle. The force as a vector. Newton's
equation f equals Ma, what does that mean that it 's conserved. It means that its time derivative
is zero. the time derivative of the kinetic energy is the sum over all the directions of space. The
mass times the velocity times now what is the derivative of U with respect to time well well U
varies with time for the same reason that it did before..
the time derivative of energy is equal to the summation of all the directions of the three
directions of space. x direction it varies a little bit if you move in the y direction and z direction.
the energy is conserved no matter what the force is as long as the rule is that the force on every
Aristotle 's law is a consistent mathematical law. Aristotle thought that in order to keep an
object moving you had to exert a force on it. an object moving through free space under its own
inertia will keep moving without an external force. in order to follow the system. All you need to
know is at the end at the initial starting point. the force only changes because the particle
moves and depending on where the particle is the force will change. the derivative of the force
with respect to position tells you how much the force changes when you move from one
position to another times how fast you move the x-Dt. In fact, if you look at this equation, you 'll
notice it 's correct because you can cancel out the dx. The f dt is the f by the x-dx by dt. if we
know. F of X? We also know DF by dx and the first equation up. Here tells us what the velocity is.
the op shot is. In fact we do know the jerk we a moment ago convinced ourselves that if we
know the initial position, we also know about the velocity in the acceleration. Well all that goes
in here is velocity and acceleration and knowledge of the force law. you can build up the entire
motion. If all you know is the at one instant of time. Now as I said this is a false law..
The lesson is in Newton 's equations, which are Secondorder equations which in all second
derivatives with respect to time, you need to know to get started positions and velocities. the
force law might depend not only on the position of particles, but it might depend on the different
other position relative positions and so forth.. If you know all the positions of all particles, then it
's assumed that you know the force on every single one of them due to all the others that's the
assumption of Newton. a force law like this is again unphysical. It never occurs in nature. the
components of force in a given direction are proportional to how fast the potential energy is
changing along that direction.. we 'll generalize this to many particles. In fact, we 'll. generalize it
to arbitrary systems, but let 's take the case of a single particle. The force as a vector. Newton's
equation f equals Ma, what does that mean that it 's conserved. It means that its time derivative
is zero. the time derivative of the kinetic energy is the sum over all the directions of space. The
mass times the velocity times now what is the derivative of U with respect to time well well U
varies with time for the same reason that it did before..
the time derivative of energy is equal to the summation of all the directions of the three
directions of space. x direction it varies a little bit if you move in the y direction and z direction.
the energy is conserved no matter what the force is as long as the rule is that the force on every
