Static Equilibrium

Physics 150/215 Lesson 7

�Center of Mass�Types of Motion�Torque�Types of Equilibrium

�Static�Translational - Rotational Conditions for Equilibrium�Center of Gravity�Free Body Diagrams

Center of Mass =

Average position of the masses

For example: 6 kg at x=5m & 7 kg at x=10mx coordinate of center of mass

= 65 710

6 7 100

137.69

Think of the average height of 6 monsters that are 5m high and 7 that are 10 m high

Motion of an object can be analyzed into three

types

�translation of the center of mass�rotation (rigid) about the center of mass �vibration (elastic) about center of mass

If the total force FTot= 0

acm = 0

Translational Acceleration is caused by the total force on the

object

then there is no Translational Acceleration

(acceleration of center of mass)

�Thus vcm = constant

�If velocity of center of mass is initially zero it will stay zero

�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

Fsin

Torque Tangential Force radius

= FSin rFrSin Fd

d rSin Moment / Lever Arm

�Linear = Translational �Angular = Rotational

Total Force = 0; Total Torque not zero

Total Force not 0; Total Torque = 0

If the total torque Tot= 0

angular acceleration

= 0

then there is no Rotational Acceleration

(change of angular speed)

�Thus angular speed = constant

�If angular speed is initially zero �it will stay zero

If object is RIGID If object is RIGID There will be no There will be no

vibration about center vibration about center of mass of mass

If object is RIGID If object is RIGID There will be no There will be no

vibration about center vibration about center of mass of mass

Static Equilibrium for rigid objects

vcm = 0 = 0FTot = 0Tot = 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 if

Ftot acm 0 TRANSLATIONAL EQUILIBRIUM

An object will have zero angular acceleration if the

total torque on the object is zero if

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

Ftot 0

0 = 0forces

The torque of a force about any point onthe 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 .

Center of Gravity

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

Free Body Diagrams

N1

N2

F2

F1

W1

W2