Rotational Equilibrium

Center of Gravity

• The point at which all object's weight can be considered to be concentrated.
• For symmetrical bodies with uniform density, center of gravity will be at geometric center.
• May be located outside the body of some objects.
• Bodies or systems rotate about their center of gravity.

Parallel Forces:

Forces acting in the same or opposite directions at different points on an object

Weight Vectors

• Drawn from center of gravity of object
• actually are the sum of infinite number of parallel weight vectors

Torque

• A force that produces rotation
• The product of the force and its torque (lever) arm
• T = Fr units are newtons x meters
• signs: ccw torques are considered +, cw torques are -
• direction of net torque is direction of resulting rotation

Rotational Equilibrium

• Sum of all ccw torques = sum of all cw torques
• No net torque
• Either no rotation or rotation at a constant speed

Coupled Forces

• Two forces in the same plane, acting at different points on a body, equal in magnitude, opposite in direction.
• Torque of couple = magnitude of one force x distance between forces
• Equilibrant of one couple is another couple.

Solving Rotational Equilibrium Problems

• Choose point to measure torques from that will simplify problem.
• With 2 unknown forces, measure torques from point of 1 unknown force.
• Set all ccw torques = all cw torques
• If force is not perpendicular to body, use perpendicular component of force.

Solving Combined Equilibrium Problems

• Write force equation(s)
• Choose pivot point to eliminate one unknown force from torque equation
• Write torque equation
• Solve torque equation for unknown force
• Use force equation to find other force

Vocabulary

• Center of gravity
• Parallel forces
• Torque
• Rotational equilibrium
• Coupled forces

Summary

• Objects will rotate about center of gravity
• Forces applied at a distance from pivot points are torques and cause rotation
• When ccw torques = cw torques, rotational equilibrium occurs