Work Done By Torque (8.3)
Start with W = Fs = (rF)(s/r)
= (+ if and both CCW
or both CW same direction ,
- if in opposite directions)
SI unit: J
Power P for rotational motion = W/t = (/) = in W
Example
You throw a Frisbee with an acceleration and a torqu
UCM and Newtons Second Law
In Uniform Circular Motion,
all move in a fixed
relationship
tangent to path, as always
Magnitudes of all three are constant
Fits right into Newtons Second Law we know
and can use
this to find an F, or we know all Fs and can fi
Chapter 4
Forces and Newtons Laws
The Smart Way
Treat both masses as one object
Bent x axis, + in direction of arrow
N = mgcos
Fx=+m2gm1sin km1gcos = (m1+m2)ax
ax = (m2gm1gsin km1gcos)/(m1+m2)
=g(m2 m1(sin kcos)/(m1+m2)
Pick one mass for T: +m2g T = m2ax
Speed in circular orbit: GMm/r2 = mv2/r so GM/r = v2 or
(speed of m)
g on Planet: GMm/R2 = mg or g = GM/R2
R = radius of planet, m = mass of an object near surface of
planet
Nonuniform Circular Motion (5.5)
Not part of this course
Tangential and Angular
Conservative force: W on a round trip = 0
Else nonconservative, e.g. friction, air resistance
Other forms of U coming, U = -Wcons
Conservation of Energy
W = Wcons + Wnc = -U + Wnc = K so
Wnc = U + K Emech (Framework!)
If Wnc = 0, U + K = 0 (energy conser
Nonuniform Circular Motion (5.5)
Not part of this course
Tangential and Angular Accel. (5.6)
Not included in course
Apparent Weight and
Artificial Gravity (5.7)
We already did this with the centrifuge and the space station
examples
Another example: passe
Energy Conservation
or
Newtons Laws?
Results will agree, so which is easier/faster?
Energy Conservation is easier than Newtons Second Law, so
use E.C. if you can
Easier: no vectors, initial and final states only
But less information so you may be forced
Momentum Conservation: the big deal here
1D and 2D
Elastic: Ki = Kf: if not, inelastic
Conservation of Momentum 2D (7.8)
Principle (same):
Typical vector problem: write component equations, find and
plug in components, solve to find whatever you are aske
Example: Ball Rolls Down Ramp
Ball of mass M, radius R,
from rest (Ktr,i = Krot,i = 0),
without friction or drag.
Drops a height h, rolls on ramp
As ball rolls without slipping, v = R, = v/R
0 = U + K = -Mgh + Ktr + Krot
Mgh = Mv2 + [(2/5)MR2](v2/R2);
If