How to Calculate Acceleration From Torque
In physics, the term "torque" refers to a twisting force, such as that seen in spinning car tires. For these and other spinning bodies, the "moment of inertia," which represents a given object's tendency to resist acceleration, acts to counter torque. As is often the case in physics, you can represent the relationship between these properties--torque, acceleration and the moment of inertia--using a mathematical equation, one which makes calculating acceleration from torque a relatively simple undertaking.
Instructions
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Calculate the torque of a spinning object if your physics textbook doesn't give it to you. Torque is equal to force times radius and expressed in units of "newton meters." For example, if you have a tire with a radius of 1.4 meters experiencing a force of 16.2 newtons, you can calculate its torque as follows: torque = 1.4 * 16.2 = 22.68 newton meters.
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Use mass and radius to calculate the object's moment of inertia, keeping in mind the equation I = 1/2 * M * R^2, where "M" is an object's mass in kilograms and "R" its radius in meters. For example, if your tire with radius 1.4 meters has a mass of 23.3 kilograms, you calculate its moment of inertia as follows: I = 1/2 * 23.3 * (1.4)^2 = .5 * 23.3 * 1.96 = 22.83 kilograms per meter squared.
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Determine acceleration from torque and moment of inertia. Knowing that torque is equal to moment of inertia times acceleration, rewrite the equation to reflect that acceleration is simply torque divided by moment of inertia. The acceleration for the example tire, then, is: 22.68/22.83 = .99 radians per second squared.
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Tips & Warnings
As torque always relates to spinning or rotating objects, the acceleration associated with it is always "angular" acceleration--how rapidly the speed at which it turns changes over time. Physicists measure angular acceleration in radians per second squared, where the "radian" measures a portion of a circle or arc like a "degree" would.
References
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