PHY221 Ch18: Rotational Statics II Applications: Examples: ladder and Box in truck Stability of object w/respect to gravity and CM location

PHY221 Ch18: Rotational Statics II Examples Example: Ladder of length L. Static  needed? Assume no friction on vertical wall. 

PHY221 Ch18: Rotational Statics Examples Example: Box in truck Truck accelerates forward Assume friction large enough so box doesn’t slide But: it can tip! Problem: what is the max acc. for no tipping? Draw picture with forces and choose axes (remember that accel. not zero) Force equation: Torque equation: (be careful about choosing O; not all points valid!)

PHY221 Ch18: Rotational Statics Stability Stability of equilibrium and torque: Equilibrium requires net force and net torque equal to zero on object But some configurations are stable and some unstable. Consider following 2 configs of a red bar that can freely rotate around a pivot pt O: Forces applied? Net force? Net torque? Let’s look at what happens when the red bar is pushed slightly from equil? Force point of view: Torque point of view: Relation of stability of equil. to potential energy:

PHY221 Ch18: Rotational Statics II Stability Application: Stability and CM position for object resting on surfaces (and relation to potential energy change) Look at tipping around O (clearly the interesting point here) Assume object barely off surface (so that N is all applied at O) and study motion: Now let’s relate to what happens to pot energy. On the left the rotation around O would increase or decrease the pot energy? On the right the rotation around O would increase or decrease the pot energy?