1. Torque Torque applies to a rotating rigid object (like a football) with an internal axis of rotation. A rigid object will rotate around its center of mass. If it is thrown into the air, the center of mass will follow a parabolic path (football, throwing knives, person, etc.) Torque = a quantity that measures the ability of a force to rotate an object around some axis.

2. Torque How easily an object rotates depends on how much force is applied and on where the force is applied. The farther the force is from the axis of rotation, the easier it is to rotate the object and the more torque is produced. The lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of force.

3. Torque Forces do not have to be perpendicular to an object to cause it to rotate. Ex: opening a door – easiest at the outside, harder the closer to the axis of rotation you get = decreasing the distance of the lever arm. Opening a door, but pushing at an angle up or down = harder to open because your force is not perpendicular to the object.

4. Torque The lever arm depends on the angle of the applied force. τ = Fd sin Θ Torque (greek letter tau) = force x lever arm d = the distance from the axis of rotation to the point where force is applied d sin Θ = the perpendicular distance from the axis of rotation to a line drawn along the direction of force. It is the lever arm. Units are in Nm

5. Torque

6. Torque is a vector quantity. Convention says that torque is: -positive if the rotation is counterclockwise -negative if the rotation is clockwise

7. Torque Ex: Find the magnitude of the torque produced by a 3.0 N force applied to a door at a perpendicular distance of 0.25 m from the hinge. G: F = 3.0 N S: τ = (3.0 N)(0.25 m)(sin 90) d = 0.25 mS: τ = 0.75 Nm Θ = 90° U: τ E: τ = Fd sin Θ

8. Torque If there are more than one force acting on an object, then you need to add the separate torques to find the total torque. Ƭ = ΣƬ = Ƭ 1 + Ƭ 2 = F 1 d 1 + F 2 d 2 Make sure to check direction of force – if the forces are in opposite directions, use opposite signs!

9. Torque Efficiency is a measure of how well a machine works. It is a ratio of work output to work input. Real machines are not frictionless and lose energy. eff = W out /W in If a machine is frictionless then mechanical energy is conserved and the efficiency of the machine is 1 or 100%. Because no machine is fricitonless, the efficiency is always less than 1 (or 100%)