Torque and Rotation.

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Torque and Rotation.

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Presentation transcript:

Torque and Rotation

Torque Force is the action that creates changes in linear motion. For rotational motion, the same force can cause very different results. A torque is an action that causes objects to rotate. A torque is required to rotate an object, just as a force is required to move an object in a line.

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 or line 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.

Line of action Torque is created when the line of action of a force does not pass through the center of rotation.

Force applied must be perpendicular The lever arm is the perpendicular distance between the line of action of the force and the center of rotation

Calculating torque The torque (τ) created by a force is equal to the lever arm (r) times the magnitude of the force (F). dsin Ѳ

Torque Torque is a vector quantity (yay!) Determine the sign of torque by using the following conventions. Positive = counterclockwise Negative – clockwise To determine the sign, imagine torque is the only thing acting on an object and that the object is free to rotate. Visualize the direction that the object would rotate

Torques can be added and subtracted If more than one torque acts on an object, the torques are combined to determine the net torque. If the torques tend to make an object spin in the same direction (clockwise or counterclockwise), they are added together. If the torques tend to make the object spin in opposite directions, the torques are subtracted.

Units of torque The units of torque are force times distance, or newton-meters. A torque of 1 N-m is created by a force of 1 newton acting with a lever arm of 1 meter.

You try… A force of 50 newtons is applied to a wrench that is 30 centimeters long. Calculate the torque if the force is applied perpendicular to the wrench so the lever arm is 30 cm.

You try… A force of 50 newtons is applied to a wrench that is 30 centimeters long. Calculate the torque if the force is applied perpendicular to the wrench so the lever arm is 30 cm. 1) You are asked to find the torque. 2) You are given the force and lever arm. 3) The formula that applies is τ = rF. 4) Solve: τ = (-50 N)(0.3 m) = -15 N.m

Net torque is zero 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

Example For example, consider a 10-meter bridge that weighs 500 newtons supported at both ends. A person who weighs 750 newtons is standing 2 meters from one end of the bridge. What are the forces (FA, FB) holding the bridge up at either end?

Example For example, consider a 10-meter bridge that has a force of 500 newtons supported at both ends. A person who weighs 750 newtons is standing 2 meters from one end of the bridge. What are the forces (Fa, Fb) holding the bridge up at either end? For the bridge not to move up or down, the total upward force must equal the total downward force. This means FA + FB = 1,250 N. Unfortunately, balanced force in the vertical direction does not tell you how the force is divided between the two ends, FA and FB. Solving for the unknown forces For the bridge to be in rotational equilibrium, the total torque around any point must be zero. If we choose the left end of the bridge, the torque created by force FA is zero because its line of action passes through the center of rotation. By setting the total of the remaining torques to zero, the force on the right support (FB) is calculated to be 400 newtons. Since the total of both forces must be 1,250 N, that means the force on the left (FA) must be 850 N. This kind of analysis is used to solve many problems in physics and engineering, including how strong to make bridges, floors, ladders, and other structures that must support forces.