PH 212

Static equilibrium

A rigid object is in static equilibrium if the net torque is zero at every point on the object, and the net force on the object is zero.

Step 1: Draw an extended free-body diagram representing the forces and their locations on the object.

Step 2: Translate the diagram into its mathematical equivalent, beginning with writing the equation for net force.

Step 3: Choose a pivot point and write the equation for net torque about that point. Torques that would produce counterclockwise rotation are positive, and torques that would produce clockwise rotation are negative. In this example, all of the forces are perpendicular to the beam, so the sin q factors are just 1.

Step 4: Algebraically solve for the unknown quantity.

Sample problem: A ladder of length L leans against a wall at an angle of q. Find the minimum coefficient of friction between the ladder and ground that will keep the ladder from sliding. Assume the wall is frictionless.

Rotational dynamics

If the net torque is not zero, the system will exhibit angular acceleration. This is the rotational equivalent of Newton's second law.

The mass is replaced with the moment of inertia, and the acceleration is angular acceleration.


Sample problem: A mass m is attached to a cord wrapped around a flywheel with mass M and radius r. How fast is the mass m moving after it accelerates downward a distance h?