Physics 150250 Lesson 7 Static Equilibrium Center of

Physics 150/250 Lesson 7 Static Equilibrium ØCenter of Mass ØTypes of Motion ØTorque ØTypes of Static Equilibrium §Translational - Rotational ØConditions for Equilibrium ØCenter of Gravity ØFree Body Diagrams

Center of Mass = Average position of the masses For example: 6 kg at x=5 m & 7 kg at x=10 m x coordinate of center of mass = Think of the average height of 6 monsters that are 5 m high and 7 that are 10 m high

Motion of an object can be analyzed into three types vtranslation of the center of mass vrotation (rigid) about the center of mass vvibration (elastic) about center of mass

Translational Acceleration is caused by the total force on the object If the total force FTot= 0 then there is no Translational Acceleration (acceleration of center of mass) acm = 0

v. Thus vcm = constant v. If velocity of center of mass is initially zero it will stay zero v. There may be rotation or vibrational motion around center of mass

Rotational acceleration is caused by the total turning force = TORQUE about the center of mass.

Tangential Force Radial Force

Force r

Force (F) r

v. Linear = Translational v. Angular = Rotational Total Force = 0; Total Torque not zero Total Force not 0; Total Torque = 0

If the total torque Tot= 0 then there is no Rotational Acceleration (change of angular speed) angular acceleration = 0

v. Thus angular speed = constant v. If angular speed is initially zero vit will stay zero

If object is RIGID There will be no vibration about center of mass

Static Equilibrium for rigid objects vcm = = FTot = 0 0

Conditions for Static Equilibrium for Rigid Objects

The center of mass of an object will not accelerate if the total force on the object is zero Ftot a cm 0 TRANSLATIONAL EQUILIBRIUM An object will have zero angular acceleration if the total torque on the object is zero 0 ROTATIONAL EQUILIBRIUM

If the initial velocity of the center of mass is zero and the initial angular velocity is zero they will remain zero if Ftot and acm 0 When this is so the object is said to be in STATIC EQUILIBRIUM

Properties of Torque

The torque of a force about any point on the line of action of that force is zero . If a body is in translational equilibrium and the net torque is zero with respect to one point in the body then it is zero with respect to all. points in the body forces = 0

Center of Gravity The position where the force of gravity acts on the object or rigidly connected objects

Free Body Diagrams F 1 N 1 W 2 F 2 N 2