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.

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Example: Ladder of length L. Static needed? Assume no friction on vertical wall.

PHY221 Ch18: Rotational Statics1.

Exam

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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.

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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.

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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?