TorqueTough NutPivot PointLever ArmPerpendicular ComponentMoment of ForceChanging a TireTorque WrenchTorqueTorqueTough NutTough NutWhich of the four arrangements is best for tightening Which of the four arrangements is best for tightening a bolt?a bolt?FA B C D2/FFF2rr2/3rr4560Pivot PointPivot PointRotation of a wheel or wrench takes place with an Rotation of a wheel or wrench takes place with an axis of rotation.axis of rotation.The point where the axis intersects the object is the The point where the axis intersects the object is the pivot pointpivot point. . rrpivot pointtataLever ArmLever ArmThe tangential force acts at a distance away from the The tangential force acts at a distance away from the pivot point.pivot point.The distance from the pivot to the force is called the The distance from the pivot to the force is called the lever armlever arm, or , or moment armmoment arm..rrlever arm points out from the pivottataPerpendicular ComponentPerpendicular ComponentOnly the perpendicular component of the force can Only the perpendicular component of the force can affect the tangential acceleration.affect the tangential acceleration.For an angle (For an angle () between the force () between the force (FF) and lever arm ) and lever arm ((rr), the perpendicular component is ), the perpendicular component is FFsinsin. . rˆangle between lever arm and forceFtaMoment of ForceMoment of ForceThe force exerted on the lever arm is the moment of The force exerted on the lever arm is the moment of force.force.This is called torque (This is called torque (). ). sinrFChanging a TireChanging a TireA wheel nut needs 95 N-m of A wheel nut needs 95 N-m of torque.torque.A 45 cm wrench makes a A 45 cm wrench makes a 6767°° angle with the horizontal. angle with the horizontal.The horizontal force needed: The horizontal force needed: Fr°°N230)113sin()m45.0(mN95sinsinFrFrFTorque WrenchTorque WrenchConsider the product Consider the product rFrFsinsin..nextFrF (0.7)2rF = (1.4)rF(0.87)rF (3r/2)(F/2) =
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