phy221 ch18: rotational statics ii
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PHY221 Ch18: Rotational Statics II
Applications:1. Examples: ladder and Box in truck2. Stability of object w/respect to gravity and CM location
PHY221 Ch18: Rotational Statics II1.
Exam
ples
Example: Ladder of length L. Static needed? Assume no friction on vertical wall.
PHY221 Ch18: Rotational Statics1.
Exam
ples
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?
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!)
PHY221 Ch18: Rotational Statics2.
Stab
ility
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 II2.
Stab
ility
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?
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