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11 Formulas<br />
sin 2 x 1cos2x<br />
2<br />
cos 2 x 1cos2x<br />
2<br />
sin 2x 2 sin x cosx<br />
cos2x cos 2 x sin 2 x<br />
1 2 sin 2 x<br />
V p V o r V rel<br />
Velocity of p<br />
relative to o<br />
a p a 0 r r 2 V rel a rel<br />
p<br />
IF rigid body is rotating AND translation at the same time THEN<br />
Take moments around its cg only<br />
ELSE<br />
can also take moments about any other points on it (but<br />
change I)<br />
END IF<br />
o<br />
r<br />
<br />
Y<br />
R Y<br />
X<br />
R y<br />
R X<br />
R<br />
x<br />
y<br />
<br />
R x<br />
BODY FIXED<br />
COORDINATES<br />
This gives the relation<br />
between the rate of<br />
change with respect to<br />
time of a vector expressed<br />
in a frame of reference<br />
which is body fixed (y,x)<br />
here, to the rate of change<br />
with respect to time of the<br />
same vector expressed<br />
using an inertial frame<br />
coordinates XY.<br />
The omega here is the<br />
angular velocity of the<br />
rigid body rotation, or the<br />
body fixed coordinates,<br />
with respect to the inertial<br />
frame.<br />
d<br />
dt R X,Y d dt R x,y R X,Y<br />
<br />
R<br />
r<br />
<br />
R r<br />
r<br />
The small disk rotates<br />
at angular speed of <br />
The condition of no slip can<br />
be seen to be<br />
R r r<br />
For the sign of generalized force:<br />
If work done by force takes away<br />
energy from system, then the<br />
sign is negative, else positive. So<br />
Friction will always have negative<br />
sign, so will damping force.<br />
d<br />
dt<br />
cosxt sinxtx t<br />
d<br />
dt<br />
df<br />
dxt<br />
<br />
d<br />
dxt<br />
d<br />
cosxt <br />
dt<br />
df<br />
dxt<br />
d<br />
d<br />
cos xt<br />
dxt<br />
d<br />
xt dt<br />
xt dt<br />
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