PHY 221 Ch 18 Rotational Statics II Applications

PHY 221 Ch 18: Rotational Statics II Applications: 1. Examples: ladder and Box in truck 2. Stability of object w/respect to gravity and CM location

PHY 221 Ch 18: Rotational Statics II 1. Examples Example: Ladder of length L. Static needed? Assume no friction on vertical wall.

PHY 221 Ch 18: Rotational Statics Example: Box in truck 1. Examples • • 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? 1. Draw picture with forces and choose axes (remember that accel. not zero) 2. Force equation: 3. Torque equation: (be careful about choosing O; not all points valid!)

PHY 221 Ch 18: Rotational Statics 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: 2. Stability 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:

PHY 221 Ch 18: Rotational Statics II 2. 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 tahe clockwise rotation around O would increase or decrease the pot energy? On the right a clockwise rotation around O would increase or decrease the pot energy?