When the appropriate sign positive or negative is assigned to the magnitudes of individual torques about a specified axis, the net torque about the axis is the sum of the individual torques:. In the following examples, we calculate the torque both abstractly and as applied to a rigid body. Take the cross product of. Evaluate the magnitude of the torque using. Assign the appropriate sign, positive or negative, to the magnitude.
Sum the torques to find the net torque. Example Calculating Torque Four forces are shown in Figure at particular locations and orientations with respect to a given xy -coordinate system. Find the torque due to each force about the origin, then use your results to find the net torque about the origin.
This problem requires calculating torque. All known quantities——forces with directions and lever arms——are given in the figure. The goal is to find each individual torque and the net torque by summing the individual torques.
Be careful to assign the correct sign to each torque by using the cross product of. The torque from force 40 N in the first quadrant is given by. Note that each force that acts in the counterclockwise direction has a positive torque, whereas each force that acts in the clockwise direction has a negative torque. The torque is greater when the distance, force, or perpendicular components are greater.
Calculating Torque on a rigid body Figure shows several forces acting at different locations and angles on a flywheel. We have. We calculate each torque individually, using the cross product, and determine the sign of the torque.
Then we sum the torques to find the net torque. If we look at Figure , we see that. Taking the cross product, we see that it is out of the page and so is positive. We also see this from calculating its magnitude:. The axis of rotation is at the center of mass of the flywheel. Since the flywheel is on a fixed axis, it is not free to translate. If it were on a frictionless surface and not fixed in place,.
A large ocean-going ship runs aground near the coastline, similar to the fate of the Costa Concordia , and lies at an angle as shown below. Salvage crews must apply a torque to right the ship in order to float the vessel for transport. A force of. What is the torque about the point of contact of the ship with the ground Figure? The sign of the torque is found using the right hand rule. If the page is the plane containing.
Using the center of the meter stick as the balance means that there is no torque due to the weight of the meter stick. This will make a positive torque. On the other side of the meter stick is a spring scale a distance r from the pivot. If the meter stick is in equilibrium, then: So, pull on the spring scale to make the thing balanced.
Be sure to read the scale in units of Newtons and not grams. Measure the angle theta with a protractor. Change theta and find the new F to make it balance. Since the stuff on the right is a constant, what kind of graph could you make that would show a linear function? Think about it. Now try something else. Smilies are On. Trackbacks are Off. Pingbacks are On.
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