Thursday, July 18, 2024

What Is The Formula For Torque In Physics

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What is Torque? | Physics |

Ans : The watt, abbreviated W, is the standard unit for measuring power. James Watt, a Scottish inventor and industrialist, is honored with the units name. In your daily life, youve most likely come across the watt. Watts are commonly used to describe the power output of electrical equipment such as light bulbs and stereos.

One watt is equal to one joule of work done per second by definition. So, if P represents power in watts, E represents energy change , and t represents time in seconds, then:


Ans : Jack works harder than Jill. To lift his twice-as-massive body up the same flight of steps, Jack must exert double the force. Jill, on the other hand, is just as powerful as Jack. Jill completes one-half the work in half the time. The reduction in time compensates for the reduction in work done.

Ans : When a body does not do any work, it does not imply that it is devoid of energy. Although the body has energy, it does not perform any work for example, a book on a table has potential energy but does not perform any work.

Ans : Because the force of gravity works at right angles to the direction of motion of the satellite, the work done by it on the satellite is zero. As a result, there is no displacement in the direction of applied force. Only the direction of motion of the I satellite is affected by gravity.

Ans : The work done by a force is determined by:

  • The forces magnitude.
  • The displacements magnitude and direction
  • Determining Torque With Moment Of Inertia And Angular Acceleration

  • 1Find the moment of inertia. The amount of torque required to move an object with angular acceleration depends on the distribution of the object’s mass, or its moment of inertia, expressed in kgâm2. When the moment of inertia isn’t provided, you can also look it up online for common objects.XResearch source
  • For example, suppose you’re trying to figure out the magnitude of torque on a solid disc. The moment of inertia for a solid disc is 1 = 10 }=}=}=10}
  • 2Determine the angular acceleration. If you’re trying to find torque, the angular acceleration will typically be given to you. This is the amount, in radians/s2, that the object’s velocity is changing as it rotates.XResearch source
  • Remember that the angular acceleration can be zero if the object is moving at a constant speed and is neither speeding up nor slowing down.
  • 3Multiply the moment of inertia by the angular acceleration to find the torque. The full formula for torque using the moment of inertia and the angular acceleration is Ï Î± \alpha } , where “Ï” stands for torque, “I” stands for the moment of inertia, and “α” stands for the angular acceleration. If you’re trying to find torque, simply multiply the moment of inertia and the angular acceleration to get your result. As with other equations, if you’re trying to find one of the other values, you can re-order the equation using common algebraic principles.XResearch source
  • Programmable Electronic Torque / Angle Wrenches

    Torque measurement is conducted in the same way as with an electronic torque wrench but the tightening angle from the snug point or threshold is also measured. The angle is measured by an angle sensor or electronic gyroscope. The angle measurement process enables joints which have already been tightened to be recognized. The inbuilt readings memory enables measurements to be statistically evaluated. Tightening curves can be analyzed using the software via the integrated tightening-curve system . This type of torque wrench can also be used to determine breakaway torque, prevail torque and the final torque of a tightening job. Thanks to a special measuring process, it is also possible to display the yield point . This design of torque wrench is highly popular with automotive manufacturers for documenting tightening processes requiring both torque and angle control because, in these cases, a defined angle has to be applied to the fastener on top of the prescribed torque .

    In 1995, Saltus-Werk Max Forst GmbH applied for an international patent for the first electronic torque wrench with angle measurement which did not require a reference arm.

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    Finding Torque For Perpendicular Forces

  • 1Find the length of the moment arm. The distance from the axis or rotational point to the point where force is applied is called the moment arm. This distance is typically expressed in meters .XResearch source
  • Since torque is a rotational force, this distance is also a radius. For this reason, you’ll sometimes see it represented with an “r” in the basic torque equation.
  • 2Work out the force being applied perpendicular to the moment arm. The force applied perpendicular to the moment arm produces the greatest torque. The simplest torque equation assumes the force is being applied perpendicular to the moment arm.XResearch source
  • In torque problems, you’ll typically be given the magnitude force. However, if you have to work it out yourself, you’ll need to know the mass of the object and the acceleration of the object in m/s2. According to Newton’s Second Law, force is equal to mass times acceleration ( F
  • 4Show the direction of the force with positive or negative torque. You now know the magnitude of the torque, but you don’t know if it’s positive or negative. This depends on the direction of the rotation. If the object is rotating counterclockwise, the torque is positive. If the object is rotating clockwise, the torque is negative.XResearch source
  • For example, if the object is moving clockwise and the magnitude of the torque is 200 Nâm, you would express this as -200 Nâm of torque. No sign is necessary if the magnitude of the torque is positive.
  • Conversion To Other Units

    Torque and Equilibrium

    A conversion factor may be necessary when using different units of power or torque. For example, if rotational speed is used in place of angular speed , we multiply by a factor of 2 radians per revolution. In the following formulas, P is power, is torque, and ” rel=”nofollow”> Greek letter nu) is rotational speed.

    000 . })=}\cdot 2\pi }\cdot \nu }}.}

    The constant below changes with the definition of the horsepower for example, using metric horsepower, it becomes approximately 32,550.

    The use of other units would require a different custom conversion factor.

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    What Is Torque Example

    Torque is the measure of the force that can cause an object to rotate about an axis. … Hence, torque can be defined as the rotational equivalent of linear force. The point where the object rotates is called the axis of rotation. In physics, torque is simply the tendency of a force to turn or twist.

    Torque And Angular Acceleration

    In this section, we will develop the relationship between torque and angular acceleration. You will need to have a basic understanding of moments of inertia for this section.


    Imagine a force F acting on some object at a distance r from its axis of rotation. We can break up the force into tangential ), radial ) . , the radial component \ and the z-component \. All components of force are mutually perpendicular, or normal.)

    From Newton’s Second Law, \

    However, we know that angular acceleration, \ , and the tangential acceleration atan are related by: \

    If we multiply both sides by r , the equation becomes

    Note that the radial component of the force goes through the axis of rotation, and so has no contribution to torque. The left hand side of the equation is torque. For a whole object, there may be many torques. So the sum of the torques is equal to the moment of inertia , \ multiplied by the angular acceleration, \.

    If we make an analogy between translational and rotational motion, then this relation between torque and angular acceleration is analogous to the Newton’s Second Law. Namely, taking torque to be analogous to force, moment of inertia analogous to mass, and angular acceleration analogous to acceleration, then we have an equation very much like the Second Law.

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    Torque And Moment In The Us Mechanical Engineering Terminology

    In US mechanical engineering, torque is defined mathematically as the rate of change of angular momentum of an object . 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 applied forces to rotate an object about an axis, but not necessarily to change the angular momentum of the object .For example, a rotational force applied to a shaft causing acceleration, such as a drill bit accelerating from rest, results in a moment called a torque. By contrast, a lateral force on a beam produces a moment , but since the angular momentum of the beam 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.

    Solved Example On Torque Formula

    Introduction to torque | Moments, torque, and angular momentum | Physics | Khan Academy

    Q1. A car mechanic applies a force of 800 N to a wrench for the purpose of loosening a bolt. He applies the force which is perpendicular to the arm of the wrench. The distance from the bolt to the mechanics hand is 0.40 m. Find out the magnitude of the torque applied?

    Answer: The angle between the moment the arm of the wrench and the force is without a doubt 90°, and sin 90° = 1. The torque is:

    T = F × r × sinTherefore, magnitude of the torque = = 320 NmHence, the magnitude of the torque is 320 Nm.

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    What Is A Gyroscopic Moment

    Gyroscopic motion is the tendency of a rotating object to maintain the orientation of its rotation. A rotating object possesses angular momentum and this momentum must be conserved. The object will resist any change in its axis of rotation, as a change in orientation will result in a change in angular momentum.

    What Is The Unit Of Torque

    Torque is represented by the Greek letter tau: \ in calculations. When it is called the moment of force, it is represented by \ Torque is equal to the dot product between force and position vector. The SI unit of force is newton \,\) and the SI unit of distance is meter. Thus,

    Thus, the International System of Measurement units used for torque is newton-meter or \.

    Although the newton meter is equal to joules, which is the SI unit for energy or Work, Torque is measured in terms of newton-meter only.

    In the imperial system, torque is measured in terms of pound-force-feet \}\) which might be abbreviated as pound-foot, with the force implied.The dimensions of torque is \

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    Derive Formula Of Torque As The Cross Product Of Force And Lever Arm Length

    This derivation of the T formula is based on our understanding of Torque as the Moment of force. When a Force is applied on a particle and that particle starts to rotate or tends to rotate about an axis then it is generally said that a Moment of force is generated. The lever arm is the perpendicular distance from the axis of rotation to the point where the force is exerted. If the force is applied perpendicular to the radius of rotation then the entire force F is responsible for the rotation But if the force is not perpendicular, the perpendicular component of the force must be found. Because this is the component that causes rotation in this case.

    The force is perpendicular to the radius of rotation. Max Torque = F rThe force is not perpendicular to the radius here. See the diagram below for resolved components of force FThus we get Torque = r F sin = r X F

    Torque Formula In Physics

    Torque Definition

    Torque is a type of measurement that can be applicable for an object which rotates about an axis. You all know that force is the only factor in linear kinematics that causes acceleration of a body.

    Just like force, Torque is involved with an angular acceleration of the body. The axis of rotation is a point where a body begins its rotation. In this article, we will read in brief regarding the torque formula physics. Physics has a simple explanation of the torque that is the tendency of a force that promotes twisting.

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    What Is An External Force

    We studied in the chapter laws of motion that when a force is applied to any object of mass, the object starts accelerating. The statement can be represented by the equation: H= k x b

    Where b is the acceleration, H is the force, k is the mass

    Similarly, When you switch on a fan, the center of the fan remains unmoved, while the fan rotates with angular acceleration. Now this center that remains unmoved is the center of mass of the fan that remains at rest. You might be wondering that the force we studied in the above relation H=k x b was for applying a force to the bodies in linear motion, then which kind of force is responsible for producing angular acceleration?

    Frequently Asked Questions On Torque

    Lets look at some of the frequently asked questions about Torque:

    Q.1. What is torque in a human body?Ans: Torque is the driving force for human movement. Being able to manipulate the target muscle torque will allow for a more specific intervention. The moment arm of a force system is the perpendicular distance from an axis to the line of action of a force. Muscle torque is the force applied by the muscles through a moment arm of a given length at a given angle to the joint.

    Q.2. What is torque in simple terms?Ans: Torque is a measure of the force that can cause an object to rotate about an axis. Just as force causes an object to accelerate in linear kinematics, torque causes an object to acquire angular acceleration.

    Q.3. Where is torque used?Ans: The most obvious example of torque in action is the operation of a crescent wrench loosening a lug nut, a playground seesaw, a doorknob, opening a soda bottle, and even in-car engines and steering wheels.

    Q.4. How is torque calculated?Ans: Torque formula can be given as:\The direction of the torque vector is found by convention using the right-hand rule.

    Q.5. What is better hp or torque?Ans: Torque is the ability of a vehicle to perform work specifically, the twisting force applied by the crankshaft. Horsepower is how rapidly the vehicle can perform that work. Torque multiplied by rpm returns horsepower. As there is a limit on how fast you can spin an engine, having higher torque allows for greater horsepower at lower rpm.

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    You Come Across These Objects Daily But Are They Point

    Well, the objects we see in real-life arent point-sized in an absolute sense. These objects have a bounded size, made up of very large particles.

    Here, we would extend the application of Newtons laws of motion to describe the rotational motion of these finite-sized objects. Since there are many particles inside the object interacting with each other, these interacting particles together form a system. Thus, any object of finite size forms a system.

    A large body that is made of many particles has a center of mass which states that the mass of the system of the body is supposed to be concentrated at the center. If an external force is applied then the center of mass remains the same or unaffected.

    What Is Torque In Physics

    Torque Basics And Formula With Examples

    Torque is the turning effect of force, it is also known as the moment of the force. Torque is the vector Quantity. Torque symbol is . The formula of Torque is , Where F is the Force and L is the moment of the arm. Torque Unit is Nm. Some Torque Examples are also Given in the post also. Keep reading


    We open or close a door by pushing or pulling it. Here push or pull turn the door about its hinge or axis of rotation. The door is opened or closed due to the turning effect of the force acting on it.

    Before we go to learn about we will learn a few terms related to torque. See also: states of equilibrium

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    The Vocabulary For Torque Physics

    The torque equation is jam-packed with important information about how torque is generated, and how to calculate a net torque. Understanding the terms in the equation will help you complete a general net torque calculation.

    First, the axis of rotation is the point about which the rotation will occur. For the wrench torque example, the axis of rotation was through the center of the bolt, since the wrench will rotate around the bolt. For a see-saw, the axis of rotation is the middle of the bench, where the fulcrum is placed, and the children at the ends of the see-saw are applying the torque.

    Next, the distance between the axis of rotation and the applied force is called the lever arm. Determining the lever arm can be tricky because it is a vector quantity, thus there are potentially many possible lever arms, but only one correct one.

    Lastly, the line of action is an imaginary line that can be extended from the applied force in order to determine the lever arm.

    Things To Remember About Torque

    • Torque is also known as a moment of force.
    • The rotating equivalent of linear motion mass is known as the moment of inertia.
    • Formula of torque is = F x r x Sin.
    • Torque is the twisting force applied by the crankshaft, which is a measure of a vehicle’s ability to perform work.
    • Horsepower refers to how quickly a vehicle can complete a task.
    • The product of torque and revolutions per minute is horsepower.
    • Because there is a limit to how rapidly an engine can spin, having more torque allows for more horsepower to be produced at lower rpm.

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