Have you ever tried to pull a stubborn nail out of a board or develop your forearm muscles by lifting weights? Both these activities involve using a "lever-type" action to produce a turning effect or torque through the application of a force. The same torque can be produced by applying a small force at a larger distance (with more leverage) or by applying a larger force closer to the point about which the object has to rotate. These two examples are shown in Fig. 1. In the case of the hammer pulling the nail, a small force applied at the end of the handle translates into a larger force being exerted on the nail at a smaller distance from the point where the nail is fixed to the board. In the second example the weight on the palm of the hand is at a greater distance from the elbow. This requires the muscles to apply a larger force at a smaller distance, usually less than 5 cm from the elbow. These are both examples of lever action—force applied at a distance from a fulcrum or pivot point or axis of rotation. A force applied as described in the above examples results in a torque on a body. Torque usually produces a rotation of a body.
Show Figure 1: Two examples of torque Torque is a measure of the turning effect of an applied force on an object, and is the rotational analogue to force. In translational motion, a net force causes an object to accelerate, while in rotational motion, a net torque causes an object to increase or decrease its rate of rotation. Torque is the product of the applied force and the perpendicular distance from the pivot point to the line of action of the force and is measured in units of N·m. where is sometimes called the "lever arm." Note: Torque has the same units as work, i.e., force times distance. Torque and work, however, are entirely different physical concepts; the fact that they have the same units is a coincidence. Consider the irregularly shaped two-dimensional object shown in Fig. 2a.
Figure 2: Illustration of lever-arm concept A force F is applied to the object at the point P, for example, by a string attached there. The object is free to rotate about the point O by a nail driven through it at that point, but not free to have translational motion. The steps needed to calculate the torque on the object about the point O are outlined below.
Figure 3: Dependence of lever arm on point of application of force Since the lever arm d makes a right angle with the line of action of the force, the three quantities, d, F, and r make a right triangle. This triangle has been redrawn in Fig. 2b. From this triangle we see that the lever arm d is given by where is the angle between r F.
Figure 4: A wheel experiencing two torques By convention, torques causing counterclockwise rotations are considered to be positive and torques causing clockwise rotations are negative. In the above exampleF1 will produce a positive or counterclockwise torque, whileF2 will produce a negative or clockwise torque. For rotation about the center the magnitude of the net torque will be the algebraic sum of the two torques:
( 4 ) As mentioned above, torque is actually a vector. The torque vector is perpendicular to the plane formed by the vectorsr andF. The right-hand rule gives the direction of the torque. Based on this rule positive torques, such as are directed out of the page, while negative torques, such as are directed into the page.Torque causes rotational motion with angular (or rotational) acceleration . where I is the moment of inertia of the system and is the angular acceleration. This equation is the angular equivalent of Newton's second law: When the net torque is zero, the object will not change its state of rotational motion—i.e., it will not start rotating or stop rotating or change the direction of its rotation. It is said to be in rotational equilibrium. If the sum of the forces acting on the object is also zero, the object is in translational equilibrium and will not change its state of translational motion, that is, it will not speed up or slow down or change its direction of motion. Whenever both of these conditions
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Procedure A: Balancing Torques
Figure 5: Three balanced torques
Figure 6: Photo of experimental set-up
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Checkpoint 1: Procedure B: Finding the Mass of a Meter StickFor this part of the experiment you will use a 200-gram mass, the meter stick and the knife edge.
Checkpoint 2: Procedure C: Determining an Unknown Mass
Figure 7: Set-up for determining an unknown mass
Figure 8: Photo of set-up for determining an unknown mass
Checkpoint 3: |