The Concept of Torque - Report Example

Torque: An overview of the In everyday life, we come across things in motion, some in linear, others in rotational. What causes the wheels of cars to rotate? One gets to think about some force that would make the wheel rotate. This force which causes objects to rotate is known as torque. A sea-saw gets balanced when the sum of clockwise torques produced by children sitting to the left side of fulcrum equalizes the sum of anticlockwise torques produced by the children sitting to the right side of fulcrum. Origin of torque: Archimedes introduced the concept of torque along with the center of gravity to the world while conducting work on levers. An author noted about Archimedes’s work in Epinions.com on 20 January 2005 that he proved that torque produced by weights scattered along the body of a lever equalizes the torque produced by sum of those weights passing through the center of gravity. Torque is the rotational / twisting force that tends to twist the object about a central point called as the pivot. It can be though of as a force along a circle. Physics suggests the word Torque for twisting force. It is r- perpendicular times F sin Θ, or F-perpendicular times r sin Θ, where the angle being considered is between r and F. In other words, it can be defined as the product of linear force when it is applied perpendicular to the radius, and the radius. It causes a change in angular velocity of a moving object, thus causing angular acceleration. Angular acceleration is affected not only by force and its direction, but also its point of application. It is an analogue for F=ma for things that are rotating. Torque is the rotational analogue of force. It is a twisting force that causes objects to spin just like a linear force that causes objects to move. The phenomenon can be explained with the help of a small experiment with a rod, whose one end is fixed to a point called fulcrum or pivot. Lets name that point as P. The other end of the rod being considered is free. The bar can be rotated about its pivot if some force is applied on the free end of the bar. Distance between the pivot “P” and the point of application of force is termed as the “radius” or the “moment arm”. The magnitude of torque applied to the object is directly proportional to the length of moment arm. That is the reason why it is easier to open a door from the handle than anywhere near the hinge. Because in the case of a door, its hinge serves the purpose of a fulcrum about which the door moves. When a door is pushed or pulled to close or open it, torque is applied on it. Therefore, as the distance between the fulcrum and the point of application of force increases, so does the torque, and if a force is applied at the hinge to move the door, it will generate no torque because of a zero moment arm. Similarly, when a wrench is rotated to tighten or loosen a nut, torque is applied on it that drives it in a circle. The harder we push or pull the wrench, the more is the torque exerted. To tighten a nut, long wrenches are preferred over short ones because they provide a room for the worker to tighten the nut by exerting lesser force on the wrench than otherwise, because torque is directly proportional to the moment arm. This radius of the bar is a vector quantity, whose magnitude is the measurement from the pivot to the point of force-application, and to show the direction, it is directed from the pivot toward the point of application of force. This direction makes this radius a vector. When a force is applied on a bar to rotate it about the pivot, not all of it is consumed in rotating the door. This force can be divided into two components, one along the bar and the other perpendicular to it. Out of the two components of the force, only the one perpendicular to the rod makes the rod rotate about its axis. Force causing the rod to rotate will always remain less than what is applied on the rod as long as the direction of the applied force remains other than perpendicular with the rod. Force applied on the rod to rotate it will be fully utilized to rotate the rod about its axis only when it is applied in a perpendicular direction to the radius of the bar. The concept of torque can be explained in another way. When a force applied on the free end of the bar is multiplied with the component of the radius making an angle of 90 degree with the force, it results into the generation of torque. Therefore torque is equal to the product of the moment arm “r”, the force “F” and “sine of the angle between r and F”. Mathematically, it can be expressed as: T= rF sin Θ. Torque is a vector quantity whose direction can be found by using the Right hand rule. While calculating torque, opposite signs are used for clockwise and anticlockwise torque. Torque and angular acceleration point in the same direction. This can be worked out through the Right hand rule. The direction of torque can be judged by pointing the fingers of the right hand in the direction of radius, and curl them in the direction of force, the vertical thumb would point in the direction of torque. The angular acceleration is zero for an object which is either at rest or moving with a uniform angular acceleration. Accordingly, there will be no torque acting on that object. Relationship between torque and force: Torque is similar to force in that it creates angular acceleration in an objects rotation just like force produces linear acceleration in translational motion of an object. Thus it serves as counterpart of force in rotation. Notation: Torque in Physics is expressed as “τ”, which is a Greek letter pronounced as “tau”. It is similar to a “T” but with a wavy top. Units of torque: Since, distance is measured in metres and force is measured in newtons. Therefore, units of torque are Nm as per the SI units and foot-pounds according to the US units. Nm is also known as Joule. But generally, Joule is not used to express torque in order to distinguish it from energy or work which are expressed in joules. Dimensions of torque: We know that: Torque = Fr = ma . r = mass * acceleration * position vector 2 -2 = [ML . T]. Torque will be zero if the angle between moment arm and force is 0 or 180 degrees because sin (0) = 0. Similarly, sin (180) = 0, and torque is equal to the product of moment arm and force when there is an angle of 90 degrees between the two. Influence of moment of inertia on torque: The rotational mass of an object is termed as its moment of inertia. It has a great influence on torque. If an object has a large moment of inertia, greater force will be required to rotate that object or stop its rotation as compared to an object whose moment of inertia is less. Moment of inertia is related to the mass of an object and its distribution along the object impacts torque applied on it. If the mass of object is concentrated near the fulcrum, rotating such an object is easier as compared to an object whose mass is majorly distant from the rotational axis. Conditions of equilibrium: An object experiences equilibrium when the following conditions are met: 1. Total forces acting on the object cancel each other. 2. Total torque / rotational forces acting on the object nullify each other. According to Lebon, 2010, the condition of rotational equilibrium when the net torque about all axes in a system is equal to zero, is also termed as the principle of moments. For a condition to achieve the condition of rotational equilibrium, it is imperative that the sum of clockwise torques balance out the sum of anticlockwise torques. Torque measuring instruments: Various instruments meant for measuring torque are available in the market nowadays. A few of them as mentioned on the Norbar website are torque wrenches, hand torque multipliers, powered multipliers, dial indicating torque wrenches and hydraulic equipment. “Norbar manufacture an extensive range of high quality torque wrenches to cover torque values from 1 N.m to 1500 N.m.” (Norbar torque tools ltd.) Benefits of torque: The concept of torque has been applied in various machines we use in our everyday life. Anything that has a motor has a torque. In automobile industry, it is the second name for power. This power is actually the torque that drives the car through the rotation of wheels. It depends on the amount of power needed by a vehicle to pull the load. Pullying trailors require a lot of torque to function. References: Lebon, Bruno. 12 Feb 2010. “Dynamic equilibrium”. 07 March 2010. . www.norbar.com. 07 March 2010. . www.epinions.com, 05 Jan. 2005. “Archimedes: The Last Great Mathematician of the Ancient World.” 07 March 2010. . Read More