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In physics and mechanicstorque is the rotational equivalent of linear force. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation.

When being referred to as moment of force, it is commonly denoted by M. In three dimensions, the torque is a pseudovector ; for point particlesit is given by the cross product of the position vector distance vector and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector [2] connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors.

In symbols:. For more on the units of torque, see Units. James Thomsonthe brother of Lord Kelvinintroduced the term torque into English scientific literature in This article follows the definition used in US physics in its usage of the word torque.

In US mechanical engineering, torque is defined mathematically as the rate of change of angular momentum Brad Point Drill Bits For Wood Group of an object in physics it is called "net torque". The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing. Moment is the general term used for the tendency of one or more spur point drill bits 400 forces to rotate spur point drill bits 400 object about an axis, but not necessarily to change the angular momentum of the object the concept which is called torque in physics.

By contrast, a lateral force on a beam produces a moment spur point drill bits 400 a bending momentbut since the angular momentum of the spur point drill bits 400 is not changing, this bending moment is not called a torque.

Similarly with any force couple on an object that has no change to its angular momentum, such moment is also not called a torque. A force applied perpendicularly to a lever multiplied by its distance from the lever's fulcrum spur point drill bits 400 length of the lever arm is its torque.

A force of three newtons applied two meters from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from the fulcrum. The direction of the torque can be determined by using the right hand grip rule : if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque.

More generally, the torque on a point particle which has the position r in some reference frame can be defined as the cross product :. Any force directed parallel to the particle's position vector does not produce a torque. It follows from the properties of the cross product that the torque vector is perpendicular to both the position and force vectors. Conversely, the torque vector defines the plane in which the position and force vectors lie. The resulting torque vector direction is determined by the right-hand rule.

The net torque on a body determines the rate of change of the body's angular momentum. It follows that. This equation is the rotational analogue of Newton's Second Law for point particles, and is valid for any type of trajectory. This arises from the fact that although spur point drill bits 400 is always conserved, the moment of inertia in general is spur point drill bits 400. The time-derivative of this is:.

This result can easily be proven by splitting the vectors into components and applying the product rule. Therefore, torque on a particle spur point drill bits 400 equal to the first derivative of its angular momentum with respect to time.

The proof can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass.

The traditional Imperial and U. Confusingly, in US practice torque is most commonly referred to as the foot-pound denoted as either lb-ft or ft-lb and the inch-pound denoted as in-lb.

A very useful special case, often given as the definition of torque in fields other than physics, is as follows:. The construction of the "moment arm" is shown in the figure to the right, along with the vectors r and F mentioned above. The problem with this definition is that it does not give the direction of the torque but only the magnitude, and hence it is difficult to use in three-dimensional cases. If the force spur point drill bits 400 perpendicular to the displacement vector rthe moment arm will be equal to the distance to the centre, and torque will be a maximum for the given force.

The equation for the magnitude of a torque, arising from a perpendicular force:. For example, if a person places a force of 10 N at the terminal end of a wrench that is 0. For an object to be in static equilibriumnot only must the sum of the forces be zero, but Brad Point Drill Bits For Wood Road also the sum of the torques moments about any point. That is, to solve statically determinate equilibrium problems in two-dimensions, three equations are used.

When the net force on the system is zero, the torque measured from any point in space is the same. For example, the torque on spur point drill bits 400 current-carrying loop in a uniform magnetic field is the same regardless of your point of reference.

Torque forms part of the basic specification of an engine : the power output of an engine is expressed as its torque multiplied by its rotational speed of the axis. Internal-combustion engines produce useful torque only over a limited range of rotational speeds typically from around 1,—6, rpm for a small car.

One can measure the varying torque output over that range with a dynamometerand show spur point drill bits 400 as a torque curve. Steam engines and electric motors tend to produce maximum torque close to zero rpm, with the torque diminishing as rotational speed rises due to increasing friction and other constraints. Reciprocating steam-engines and electric motors can start heavy loads from zero rpm spur point drill bits 400 a clutch.

If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through a rotational distance, it is doing work. Mathematically, for rotation about a fixed axis through the center of massthe work W can be expressed spur point drill bits 400. An alternate expression for the same scalar triple product is. Since the parameter of integration has been changed from linear displacement to angular displacement, the limits of the integration also change correspondingly, giving.

If the torque and the angular spur point drill bits 400 are in the same direction, then the scalar product reduces to a product of magnitudes; i. It follows from the work-energy theorem that W also represents the change in the rotational kinetic energy E r of the body, given by. Power is the work per unit timegiven by. Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. Note spur point drill bits 400 the power injected by the torque depends only on the instantaneous angular speed — not on whether the angular speed increases, decreases, or remains constant while the torque is being applied this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed — not on the resulting acceleration, if any.

In practice, this relationship can be observed in bicycles : Bicycles are typically composed of two road wheels, front and rear gears referred to as sprockets meshing with a circular chainand a derailleur mechanism if the bicycle's transmission system allows multiple gear ratios to be used i. A cyclistthe person who rides the bicycle, provides the input power by turning pedals, thereby cranking the front sprocket commonly referred to as chainring.

The input power provided by the cyclist is equal to the product of cadence i. The bicycle's drivetrain transmits the input power to the road wheelwhich in turn conveys the received power to the road as the output power of the bicycle.

Depending on the gear ratio of the bicycle, a torque, rpm input pair is converted to a torque, rpm output pair. By using a larger rear gear, or by switching to a lower gear in multi-speed bicycles, angular speed of the road wheels is decreased while the torque is increased, product of which i.

Consistent units must be used. For metric SI units, power is wattstorque is newton metres and angular speed is radians per second not rpm and not revolutions per second.

Also, the unit newton metre is dimensionally spur point drill bits 400 to the joulewhich is the unit of energy.

However, in the case of torque, the unit is assigned to a vectorwhereas for energyit is assigned to a scalar. This means that the dimensional equivalence of the newton metre and the joule may be applied in the former, but not in the latter case.

This problem is addressed in orientational analysis which treats radians as a base unit rather than a dimensionless unit. A conversion factor may be necessary when using different units of power or torque. Some people e. This results in the formula changing to:.

The constant below in foot-pounds per minute changes with the definition of the horsepower; for example, using metric horsepower, it becomes approximately 32, The use of other units e. For a rotating object, the linear distance covered at the circumference of rotation is the product of the radius with the angle covered. These two values can be substituted into the definition of power :.

The radius r and time t have dropped out of the equation. However, angular speed must be spur point drill bits 400 radians per unit of time, by the assumed direct relationship between linear speed and angular speed at the beginning of the derivation. If torque is in newton metres and rotational speed in revolutions per second, the above equation gives power in newton metres per second or watts. If Imperial units are used, and if torque is in pounds-force feet and rotational speed in revolutions per minute, the above equation gives power in foot pounds-force per minute.

The Principle of Moments, also known as Varignon's theorem not to be confused with the geometrical theorem of the same name states that the sum of torques due to several forces applied to a single point is equal to the torque due to the sum resultant of the forces.

Mathematically, this follows from:. From this it follows that if a pivoted beam of zero mass is balanced with two opposed forces then:. Torque can be multiplied via three methods: by locating the fulcrum such that the length of a lever is increased; by using a longer lever; or by the use of a speed reducing gearset or gear box. Such spur point drill bits 400 mechanism multiplies torque, as rotation rate is reduced.

From Wikipedia, the free encyclopedia. For other uses, see Torque disambiguation. Physics concept. Second law of motion. History Timeline Textbooks. Newton's laws of motion. Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton—Jacobi equation Appell's equation of motion Koopman—von Neumann mechanics.

Core topics. Motion linear Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration.

Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed. See also: Couple mechanics.

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