Let us take the origin
of the xyz coordinate system
at the center of the wheel,
the positive x axis
in the direction of the angular momentum vector
L
and the positive z axis
in the direction opposite to that of the weight vector
G.
With those choices the positive y axis
runs along the wheel, pointing towards us.
In those coordinates the weight vector
G
does not cause any torque
since it acts in the origin.
However, with
d
= ( d , 0 , 0 )
and
R
= ( 0 , 0 , R )
d
representing the position where the axis is attached to the rope,
we have
τ
=
d
×
R
= ( d , 0 , 0 ) × ( 0 , 0 , R )
= ( 0 , -dR , 0 )
Hence, the torque
τ
acts in the negative y direction.
|
|
