Torque Rotational Dynamics

There are 3 types of motion Translational Rotational Vibrational

The cause of motion

If the object is being moved by a force (translational motion), the force is doing work The ability of the force to move an object = work

Cause of rotation

The ability of a force to move an object = TORQUE

The amount of torque depends on where and in what direction the force is applied, as well as the location of the axis of rotation.

9.1 The Action of Forces and Torques on Rigid Objects DEFINITION OF TORQUE Magnitude of Torque = (Magnitude of the force) x (Lever arm) LA = shortest distance from the axis of rotation to the line of the force SI Unit of Torque: newton x meter (N·m)

Example 2 The Achilles Tendon The tendon exerts a force of magnitude 790 N. Determine the torque (magnitude and direction) of this force about the ankle joint.

The sign of torque CW = “—”, CCW – “+”

Example:

New meaning of “EQUILIBRIUM No motion (W net =0) No rotation ( )

Example 3 A Diving Board A woman whose weight is 530 N is poised at the right end of a diving board with length 3.90 m. The board has negligible weight and is supported by a fulcrum 1.40 m away from the left end. Find the forces that the bolt and the fulcrum exert on the board.

Example Predict in which case the required F is smaller. Calculate the required force in each design.

Example A 1220-N uniform beam (center of mass is in the middle) is attached to a vertical wall at one end and is supported by a cable at the other end. A 1960-N crate hangs from the far end of the beam. Using the data shown in the drawing, find (a) the magnitude of the tension in the wire and (b) the magnitude of the horizontal and vertical components of the force that the wall exerts on the left end of the beam.

A 5.0 m long horizontal beam weighing 315 N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53 degrees with the horizontal, and a 545 N person is standing 1.5 m from the wall. Find the force in the cable, F t, and the force exerted on the beam by the wall, R, if the beam is in equilibrium R 545N315N FtFt