Missing Affiliations: Undisclosed relationship to topics. Other: Other flag. Follow Us. Download Our App. Sign In. UserName, Email or phone. Enter your password.
Remember me. Register Forgot password. The torque produced by a force is found by multiplying the perpendicular distance between the line of force and the axis of rotation. Alternatively, one could take the force component perpendicular to the shortest line between the axis of rotation and the point of application of the force, and then multiply this component by the length of the shortest line.
This is depicted in the diagram below:. Torque is given by , and the shortest distance between the axis of rotation and the point of application of the force is. The force is and the force component perpendicular to the shortest line between the axis of rotation and the point of application is.
Then, the torque is given by. Torque is mathematically defined as the rate of change of angular momentum of and object. It can be clearly seen that this is compatible with the force — linear momentum relationship in linear movements. The torque is also equal to the product of the moment of inertia and the angular acceleration. Torque is a vector with the direction determined by the cross product of the force and distance. It is perpendicular to the plane of rotation.
Torsion is experienced in day to day activities such as tightening a screw or twisting a cloth. Torsion is the deformation of objects due to a pair of equal and opposite torques. The relationship between torque and shear stress is detailed in section 5. In this equation, J denotes the second polar moment of area of the cross section. This is sometimes referred to as the " second moment of inertia ", but since that already has a well-established meaning regarding the dynamic motion of objects, let's not confuse things here.
We'll discuss moment's of area in more detail at a later point, but they take on a very simple form for circular cross sections:. Now we have equations for our shear strain and our shear stress, all that is left to do is use Hooke's law in shear to see how they are related. Hooke's law lets us write down a nice equation for the angle of twist — a very convenient thing to measure in lab or our in the field. And, just like we saw for axial displacements , we can use superposition for our shear deformations as well:.
This final equation allows us to split up torques applied to different parts of the same structure. Let's work out a problem, and see if we understand what's going on for torsional deformations.
One of the most common examples of torsion in engineering design is the power generated by transmission shafts. We can quickly understand how twist generates power just by doing a simple dimensional analysis.
At the outset of this section, we noted that torque was a twisting couple, which means that it has units of force times distance, or [N m]. So, by inspection, to generate power with a torque, we need something that occurs with a given frequency f , since frequency has the units of Hertz [Hz] or [s -1 ].
0コメント