Newtonian Mechanics: Rectilinear motion

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Newtonian Mechanics Rectilinear motion
What are Newtons three laws of motion?
What are these derived from?
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Newtons First law
To apply Newtons laws in a non-inertial
reference frame we need to introduce fictitious
forces
If we are in a rotating frame ,for example, we
can use Fma if we use a modified force,
FFrealFfict,
What does this say about when it is reasonable to
approximate a rotating frame as an inertial frame?
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Newtons Second and Third Laws
The time rate of change of an objects linear
momentum is proportional to the total applied
force
Fd(mv)/dtdp/dt
Two interacting bodies exert equal and opposite
forces upon each other.
F1-F2
Then by above, dp1/dtdp2/dt0, so d(p1p2)/dt0,
so p1p2constant. Special case of the law of
conservation of linear momentum.
4
Newtons Second and Third Laws
The time rate of change of an objects linear
momentum is proportional to the total applied
force
Fd(mv)/dtdp/dt
Two interacting bodies exert equal and opposite
forces upon each other.
F1-F2
Then by above, dp1/dtdp2/dt0, so d(p1p2)/dt0,
so p1p2constant. Special case of the law of
conservation of linear momentum.
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Constant acceleration equations
We can now write down equations of motion, from
Fma
And solve rather simply for constant
acceleration!
6
Atwoods machine
A massless pulley hangs from a fixed support. A
massless strong connecting two (possibly) unequal
masses hangs over the pulley. Find the
acceleration of the masses and the tension in the
string. (Make sure to check your answers in
limiting cases) (If you finish early, consider a
double-atwood machine, where one mass is
replaced by a second pulley with two masses, and
find the acceleration of all three masses)
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Sliding down a plane
A block starts at rest and slides down a
frictionless place inclined at an angle. What
should the angle be so that the block travels a
given horizontal distance in the minimum amount
of time? What if there is friction between the
block and the plane?