Torque

What do you think? Doorknobs come in a variety of styles. Describe some that you have seen. Which style of doorknob is easiest to use? Why?

Rotational and Translational Motion Consider a tire on a moving car. Translational motion is the movement of the center of mass. The entire tire is changing positions. Rotational motion is the movement around an axis. Rotation occurs around a center. Changes in rotational motion are caused by torques. Torque is the ability of a force to affect rotation.

Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related

Torque The door is free to rotate about an axis through O There are three factors that determine the effectiveness of the force in opening the door: The magnitude of the force The position of the application of the force The angle at which the force is applied

Torque, cont Torque, t, is the tendency of a force to rotate an object about some axis t = r F t is the torque symbol is the Greek tau F is the force r is the length of the position vector SI unit is N.m

Direction of Torque Torque is a vector quantity The direction is perpendicular to the plane determined by the position vector and the force If the turning tendency of the force is counterclockwise, the torque will be positive If the turning tendency is clockwise, the torque will be negative

Torque as a Vector Are the torques shown to the right positive or negative? The wrench produces a positive torque. The cat produces a negative torque. Net torque is the sum of the torques. Torque is a vector quantity. A counterclockwise rotation means torque will be positive. A clockwise rotation means torque is negative.

Multiple Torques When two or more torques are acting on an object, the torques are added As vectors If the net torque is zero, the object’s rate of rotation doesn’t change

General Definition of Torque The applied force is not always perpendicular to the position vector The component of the force perpendicular to the object will cause it to rotate

General Definition of Torque, cont When the force is parallel to the position vector, no rotation occurs When the force is at some angle, the perpendicular component causes the rotation

General Definition of Torque, final Taking the angle into account leads to a more general definition of torque: t = r F sin q F is the force r is the position vector q is the angle between the force and the position vector

Lever Arm The lever arm, d, is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force d = r sin q

Torque Where should the cat push on the cat-flap door in order to open it most easily? The bottom, as far away from the hinges as possible Torque depends on the force (F) and the length of the lever arm (d). Is the Pushed on the door with the same force but out of the way closer to the hinge the door would be more difficult to rotate. How easily an object rotates depends not only on how much force is applied but also on where the forces 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 perpendicular distance from the axis of rotation tool line drawn along the direction of force is called the lever arm. The letter d is the perpendicular distance from the axis of rotation to the line along which the life force acts.

Right Hand Rule Point the fingers in the direction of the position vector Curl the fingers toward the force vector The thumb points in the direction of the torque

Net Torque The net torque is the sum of all the torques produced by all the forces Remember to account for the direction of the tendency for rotation Counterclockwise motions are positive Clockwise motions are negative

Practice Problems Suppose the force on the wrench is 65.0 N and the position vector (r) is 20.0 cm. The angle () between the force and r is 35.0°. Calculate the torque. Answer: 7.46 N•m What force would be required to produce the same torque if the force was perpendicular to the position vector? Answer: 37.3 N r d

Practice Problems Suppose the force on the wrench is 65.0 N and the position vector (r) is 20.0 cm. The angle () between the force and r is 35.0°. Calculate the lever arm. Answer: 0.115 m What force would be required to produce the same torque if the length of the position vector was 15.0 cm? Answer: 86.7 N r d