Static Equilibrium Physics 150/250 Center of Mass Types of Motion Torque Types of Static Equilibrium Translational - Rotational Conditions for Equilibrium Center of Gravity Free Body Diagrams 1

Average position of the masses Center of Mass = Average position of the masses For example: 6 kg at x=5m & 7 kg at x=10m x coordinate of center of mass = Think of the average height of 6 monsters that are 5m high and 7 that are 10 m high 2

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 3

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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 5

If velocity of center of mass is initially zero it will stay zero 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 6

Rotational acceleration is caused by the total turning force = TORQUE about the center of mass. 7

Tangential Force Radial Force 8

Force r 9

Force (F) r 1 0

1 1

Linear = Translational Angular = Rotational Total Force = 0; Total Torque not zero Total Force not 0; Total Torque = 0 1 2

angular acceleration  = 0 If the total torque Tot= 0 then there is no Rotational Acceleration (change of angular speed) angular acceleration  = 0 1 3

Thus angular speed  = constant If angular speed is initially zero it will stay zero 1 4

There will be no vibration about center of mass If object is RIGID There will be no vibration about center of mass 1 5

Static Equilibrium for rigid objects vcm = 0  = 0 FTot = 0 Tot = 0 1 6

Equilibrium for Rigid Objects 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   TRANSLATIONAL EQUILIBRIUM cm An object will have zero angular acceleration if the total torque on the object is zero           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  thus acm    thus a 0 When this is so the object is said to be in STATIC EQUILIBRIUM

Properties of Torque 18

t t = = forces 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 . t t = = forces 1 9

Center of Gravity The position where the force of gravity acts on the object or rigidly connected objects 2 0

Free Body Diagrams F1 N1 N2 W1 W2 F2 2 1