Calculating the torque of a wheel wrench

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We are daily exposed to simple systems that must be rotated. As an example, we can mention the act of opening canned food lids, doors, pliers, wheel wrenches, etc. O torque is the quantity related to the rotation of a system. For rotation, it is necessary to apply a torque.

Also called moment of strength, the torque is a Vector greatness that results from the product between a strength applied perpendicularly to a point and the distance from the region of application of the force and the axis of rotation.

M = F. x

The terms of the equation and the respective units of measure are:

M = Torque or moment of force (N.m);

F = Force applied (N);

x = Lever arm (m): distance between the point of application of force and the axis of rotation.

The longer the lever arm, the less force it takes for the system to rotate. More effort will be required to generate rotation if the force is applied too close to the axis of rotation. If the door handles were fixed close to the hinges, which are the axes of rotation, the force made to rotate a door to open or close it would be too great. That's why

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the handles are installed as far away from the hinges as possible, requiring less effort to move the door.

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The Wheel Wrench Case

Imagine that a driver needs to change the tire bored of a car. Typically, this type of work is performed with a wheel wrench similar to this one:

For best efficiency, the driver must force the ends of the tool, turning it with both hands in the same direction.

idealized situation

Imagine that the torque required for a wheel bolt to rotate is 100 N.m. By pushing with both hands 40 cm (0.4 m) from the center of rotation, a driver tries to remove the screws. What force would be required to be applied by each hand in order to rotate the system?

Adopting the counterclockwise direction of rotation as positive, the torque is determined as follows:

M = F. x

100 = F. 0,4

F = 100 ÷ 0.4

F = 250 N

We can conclude that the force made by each of the hands in the rotation is 250 N, totaling a force of 500 N for the system to rotate.

Using both hands to rotate the system will always be more effective than using only one hand, as shown in the image above.


By Joab Silas
Graduated in Physics

Would you like to reference this text in a school or academic work? Look:

JUNIOR, Joab Silas da Silva. "Calculating the torque of a wheel wrench"; Brazil School. Available in: https://brasilescola.uol.com.br/fisica/calculando-torque-uma-chave-roda.htm. Accessed on June 27, 2021.

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