Understanding Torque and Reference Frames in Rotational Motion

In summary: If you are picturing the left end as being anchored, then it would be counter-clockwise for the reference frame. If you are picturing the left end as being unanchored, then it would be clockwise for the reference frame.Hi,I was wondering if torque is affected by the frame of reference.Suppose I have a rod of length L and I want to apply a torque of magnitude T to the right end. If I apply the torque in the frame of reference where the right end is anchored, then the torque will be T x L. However, if I apply the torque in the frame of reference where the right end is unanchored, the torque will be -T x L.
  • #1
tomizzo
114
2
Hello,

I have a question regarding the concept of torque and reference frames.

Say for example I have a rod of length L and that the rod has it's right side anchored to act as a pivot point. Now let's say that I input a force on the left side of the bar in an upward direction. Assuming that positive torque corresponds to clockwise rotation, the torque is the force x L (and is positive) with respect to the right pivot point..

Now let's say I do this same experiment, but this time, I want to use a frame of reference such that the left side of the rod appears to be anchored. From what I can deduct, the torque as seen by this virtual pivot point will have the same torque magnitude as the last experiment, except it will be negative now...

Is my reasoning correct? I'm kind of just curious and don't know if phenomenon has a specific name.

Thanks for any help!
 
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  • #2
You are correct in the sense that as long as you consistently designate one direction as positive and the other as negative the results will be consistent up to that change in sign. Usually one designates counter-clockwise rotation as positive (that is, opposite of your choice above) since this corresponds to the right-hand rule [1], but that is just a practical convention that gives a consistent relation between linear direction of the axis with direction of rotation around those axis.

[1] http://en.wikipedia.org/wiki/Right-hand_rule
 
  • #3
The motion of the bar from the point of view of the unanchored end will also be clockwise rotation. So, the fictitious torque in this frame will have the magnitude and direction as the true torque in the original frame.
 
  • #4
Hi Perok,

I can't visualize how the torque would be in the same direction... I keep picturing the bar would have to be rotated counter clockwise to keep the left end in place for our reference frame. Could you explain further?
 
  • #5
If the bar starts horizontal and you rotate the left end clockwise by 90°, then the left end is above the right end.

If you imagine the left end is fixed, and rotate the right end clockwise by 90°, then again the left end is above the right. Same as before.

I'm not sure what you're picturing.
 

FAQ: Understanding Torque and Reference Frames in Rotational Motion

1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is represented by the symbol "τ" and is calculated as the product of the force applied and the distance from the axis of rotation.

2. What is the difference between torque and force?

While force is a push or pull that causes an object to accelerate, torque specifically refers to the rotational effect of a force. It is dependent on both the magnitude of the force and the distance from the axis of rotation.

3. How do reference frames affect torque?

Reference frames, or the point from which we measure an object's position and motion, can affect torque in two ways. First, the axis of rotation can change depending on the reference frame, which can impact the calculation of torque. Second, the direction of the force may be different in different reference frames, which can also affect the torque.

4. Can torque be negative?

Yes, torque can be negative. This occurs when the direction of the force and the direction of the rotation are opposite. In this case, the torque is calculated as a negative value and indicates that the rotation is in the opposite direction of the applied force.

5. How is torque used in real-life applications?

Torque is used in many real-life applications, including engineering, physics, and mechanics. It is essential in designing and understanding the operation of machines and structures that involve rotational motion, such as engines, gears, and levers. Torque is also important in sports, such as baseball and golf, where the rotation of an object is critical for its performance.

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