- #1
Pushoam
- 962
- 52
Homework Statement
Homework Equations
The Attempt at a Solution
Let's consider a cylindrical coordinate system whose z-axis coincides with the hinge and origin is the lowest point of the hinge.
Let's say that the truck moves along the x-axis.
W.r.t. this frame,
Torque about the hinge ## \vec \tau = \vec r \times \vec F_{n-in}
\\= [\frac w 2 \hat s + \frac h 2 \hat s ] \times [ mg (-\hat z )+m A (-\hat x)]
\\\hat x = \cos \phi \hat s+ \sin \phi \hat \phi
\\\vec \tau = \frac m 2 [ \{ wg - h \cos \phi \} \hat \phi - \hat z~w \sin \phi + h \sin \phi \hat s ]##
The body can rotate only about the hinge, so the torque should be only about the ##\hat z ## direction. I can take the component of the torque in the ##\hat \phi ## to be 0 as there is both negative and positive terms but how to make the component of the torque in the ##\hat s ## zero?