Torque,stability and equilibrium
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*door top viewF1F2axis of rotationr1r2Where:F = forcer = lever arm= perpendicular distance from the axis of rotation to the line along which the forces acts.here., F
*door top viewF1F2axis of rotationr1r2 F x r
Moment of Force or Torque ()
a vector quantity that determines the ability of a force to introduce rotation. = rF ; unit: mNMagnitude of the applied forceDistance from point of application to pivot (location of applied force)Angle ( direction of the applied force)
F1F2F3r1r2 F1 > F2 F2 < F1 = 0NOTE: in general = rFRemind us that we must use the distance from the axis of rotation that is perpendicular to the line of action of the forcer = r sin
F2 = rFl = rF sinWe can use = r F or = r F or = r F sin to calculate the torque whichever is easiest.Line of action of a force - the line of motion of a
force is an imaginary line of indefinite length drawn a long the direction of the forceThe moment arm is the perpendicular distance
from the line of action of a force to the axis of rotation.
1. An 80 N acts at the end of a 12 cm wrench as shown. Find the torque.80 N12 cm =60o 2. Find the resultant torque about axis A for the arrangement shown:
=30o =30o 4 m2 m6 mF3 = 20 NF2 = 40NF1 = 30 N
Torque is a vector quantity that has a direction as well as magnitude
Thumb F (force)Pointer r (moment arm)Middle finger direction of (torque)
Car at rest
Constant speed, no change in direction
wheel at restConstant rotation
The center of mass lies at the geometric center for a symmetric, uniform density object.
The center of mass can be outside the mass of the body.
Center of mass
Ability of an object to return to its original position after it is displaced or tilted slightly- CG is below of point of support- the objects return to its original position- When object is displaced, the object moves even farther from its position- When object is displaced, the object remain in its position