Torque

Torque By Newton’s 2nd law - Force is the action that creates changes (acceleration) in linear motion. A torque is an action that creates changes (acceleration) in rotational motion.

Torque Torque is created by force, but it also depends on where the force is applied and the point about which the object rotates. For example, a door pushed at its handle will easily turn and open, but a door pushed near its hinges will not move as easily. The force may be the same but the torque is quite different.

Center of rotation The point about which an object turns is its center of rotation. For example, a door’s center of rotation is at its hinges. A force applied far from the center of rotation produces a greater torque than a force applied close to the center of rotation.

Calculating torque The torque ( ) created by a force is equal to the lever arm (r) times the magnitude of the force (F). Ɵ is the angle between the force and the object. r is the distance between the force and the point of rotation

Units of torque The units of torque are force times distance, or Nm.

Sign Convention for Torque By convention, counterclockwise torques are positive and clockwise torques are negative. ccw Positive torque: Counter-clockwise cw Negative torque: clockwise

Net Force = 0 , Net Torque ≠ 0 10 N 10 N > The net force = 0, since the forces are applied in opposite directions so it will not accelerate. > However, together these forces will make the rod rotate in the clockwise direction.

Net torque = 0, net force ≠ 0 10 N 10 N The rod will accelerate upward under these two forces, but will not rotate.

Example A force of 50 N is applied to a wrench that is 30 centimeters long. Calculate the torque. τ = (-50 N)(0.3 m) = -15 Nm

Example A 20-centimeter wrench is used to loosen a bolt. The force is applied 0.20 m from the bolt. It takes 50 newtons to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30-degree angle from perpendicular?

Rotational equilibrium When an object is in rotational equilibrium, the net torque applied to it is zero. For example, if an object such as a see-saw is not rotating, you know the torque on each side is balanced If an object is not rotating, you can choose anywhere to be the center of rotation.

Steps Draw the object that would rotate. Draw all the forces that are acting on the object Choose a point of rotation It should be at a place where there is a force that you do not know Show the direction of rotation of each force around that point Set the CCW torques equal to the CW torques

Example W x L Given: W=50 N, L=0.35 m, x=0.03 m Find the tension in the muscle x L F = 583 N

Example Consider a 10-meter bridge that weighs 500 N is supported by two supports that are one meter from either end. A person who weighs 750 N is standing 3 meters from one end of the bridge. What are the forces holding the bridge up?

Statics Beam Problem A 4 m beam with a 30 kg mass is free to rotate on a hinge. It is attached to a wall with a horizontal cable. Find the cable tension. T θ mg θ Fx Fy 90o-θ θ + . θ = 35o Check: What is Torque from Beam’s weight when θ = 0o ?

Find the vertical and horizontal components of the hinge force and the total magnitude of the hinge force in the previous problem

Example A uniform ladder of mass 40 kg and length 10 m is leaned against a wall making an angle of 83o with the floor. A person of mass 80 kg stands on the ladder a distance 7 m from the bottom, as measured along the ladder. What is the force of friction between the floor and the ladder? What is the coefficient of friction?