Is the Proof Behind Choosing Any Point on an Axis to Calculate Torque?

In summary, to calculate the torque about an axis, one can choose any point on the axis and find the torque about that point. This can be split into two components, one parallel to the axis and the other orthogonal to it. The latter component is resisted by an equal and opposite torque from the structures holding the axis in place, such as bearings and wheel struts. Thus, when adding in the reactive torque, we are left with only the component parallel to the axis.
  • #1
Ajaysabarish97
5
0
I know that to calculate the torque about an axis, we can choose any point on that axis and find the torque about that point and take the component along the direction of the axis.Buy what is the proof behind this theorem?
 
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  • #2
Split the torque into two components, one parallel to the axis and the other orthogonal to it. Then the second one is trying to change the orientation of the axis and so will be resisted by an equal and opposite torque applied by whatever structures hold the axis in place, such as bearings and wheel struts. When we add in that reactive torque, we are left with the component parallel to the axis.
 

Related to Is the Proof Behind Choosing Any Point on an Axis to Calculate Torque?

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or a fixed point. This type of motion is characterized by the object's orientation or angular position changing over time.

2. What causes rotational motion?

Rotational motion is caused by a force acting on an object that is not directly in line with the object's center of mass. This creates a torque, or a rotational force, that causes the object to rotate around the axis.

3. What is the difference between rotational and translational motion?

Translational motion is the movement of an object in a straight line, while rotational motion is the movement of an object around an axis. In translational motion, all parts of the object move the same distance and at the same speed, while in rotational motion, different parts of the object may move at different speeds and distances.

4. How is rotational motion measured?

Rotational motion can be measured using angular velocity, which is the rate of change of angular displacement over time, and angular acceleration, which is the rate of change of angular velocity over time. These are typically measured in radians per second and radians per second squared, respectively.

5. What are some real-life examples of rotational motion?

Some examples of rotational motion in everyday life include the rotation of the Earth on its axis, the spinning of a top, the movement of a Ferris wheel, and the rotation of a bicycle wheel. In sports, the spinning of a ball, such as a basketball or a soccer ball, is also an example of rotational motion.

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