How to Calculate Torque
Identify the forces exerted on the body and their corresponding moment arms., Use the equation for torque, τ = Fr, to simply replace the variables with your given or obtained data., Make use of sign conventions (positive or negative) to show torque...
Step-by-Step Guide
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Step 1: Identify the forces exerted on the body and their corresponding moment arms.
If the force is not perpendicular to the moment arm being considered (i.e. it's mounted at an angle) you may need to find its components using trigonometric functions, such as sine or cosine.
The force component you consider will depend on the equivalent of the perpendicular force.
Imagine a horizontal bar, and you need to apply a force of 10N at an angle of 30° above the horizontal for to rotate it about its center.
Since you need to use a force that is perpendicular to the moment arm, you need a vertical force to rotate the bar.
Therefore, you need to consider the y-component, or use F = 10sin30° N. -
Step 2: Use the equation for torque
A simple example is:
Imagine a 30 kg child sitting on one side of a seesaw.
The length of one side of the seesaw is
1.5 m.
Since the rotation axis of the seesaw is at the center, you do not need to multiply the length.
You need to determine the force exerted by the child, by using mass and acceleration.
Since the given data is mass, you need to multiply it by the acceleration due to gravity, g, which is equal to
9.81 m/s2.
Therefore:
Now, you have all the needed data to use the torque equation: , When the force rotates the body clockwise, torque is negative.
When the force rotates the body counterclockwise, torque is positive.
For multiple applied forces, just sum up all of the torques in the body.
Since each force tends to produce different rotational directions, the use of sign convention is important to keep track of which forces are acting in which directions.
For example, two forces, F1=
10.0 N clockwise and F2 =
9.0 N counterclockwise, are applied to the edge of a wheel with a diameter of
0.050m.
Since the given body is a circle, its fixed axis is the center.
You need to divide the diameter and get the radius.
The measurement of the radius will serve as the moment arm.
Therefore the radius is equal to .025m.
For clarity, we can solve for the individual torques brought about by the forces.
For force 1, the action is clockwise so the torque produced is negative:
For force 2, the action is counterclockwise so the torque produced is positive:
Now we can just sum up the torques to get the net torque: -
Step 3: τ = Fr
-
Step 4: to simply replace the variables with your given or obtained data.
-
Step 5: Make use of sign conventions (positive or negative) to show torque direction.
Detailed Guide
If the force is not perpendicular to the moment arm being considered (i.e. it's mounted at an angle) you may need to find its components using trigonometric functions, such as sine or cosine.
The force component you consider will depend on the equivalent of the perpendicular force.
Imagine a horizontal bar, and you need to apply a force of 10N at an angle of 30° above the horizontal for to rotate it about its center.
Since you need to use a force that is perpendicular to the moment arm, you need a vertical force to rotate the bar.
Therefore, you need to consider the y-component, or use F = 10sin30° N.
A simple example is:
Imagine a 30 kg child sitting on one side of a seesaw.
The length of one side of the seesaw is
1.5 m.
Since the rotation axis of the seesaw is at the center, you do not need to multiply the length.
You need to determine the force exerted by the child, by using mass and acceleration.
Since the given data is mass, you need to multiply it by the acceleration due to gravity, g, which is equal to
9.81 m/s2.
Therefore:
Now, you have all the needed data to use the torque equation: , When the force rotates the body clockwise, torque is negative.
When the force rotates the body counterclockwise, torque is positive.
For multiple applied forces, just sum up all of the torques in the body.
Since each force tends to produce different rotational directions, the use of sign convention is important to keep track of which forces are acting in which directions.
For example, two forces, F1=
10.0 N clockwise and F2 =
9.0 N counterclockwise, are applied to the edge of a wheel with a diameter of
0.050m.
Since the given body is a circle, its fixed axis is the center.
You need to divide the diameter and get the radius.
The measurement of the radius will serve as the moment arm.
Therefore the radius is equal to .025m.
For clarity, we can solve for the individual torques brought about by the forces.
For force 1, the action is clockwise so the torque produced is negative:
For force 2, the action is counterclockwise so the torque produced is positive:
Now we can just sum up the torques to get the net torque:
About the Author
Rachel King
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