Find Φ at the Point of A: Question About Torque

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In summary, the conversation is about finding the value of Φ at point A on a filled pipe shaped as an incomplete cone, given a disturbed torque of M kN.m/m exerted on the pipe. The equation Φ=∫T.dx/G.J is used to integrate the torque and reach a solution, but there is uncertainty about the correctness of the answer obtained, which is 5h^2/GR^4. Further clarification and reasoning is requested.
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Homework Statement


A filled pipe shaped as a incomplete cone is shown in figure. a disturbed torque of M kN.m/m is exerted on this pipe. find Φ at the point of A. (all variable and given data is shown in figure)
http://www.radinupload.ir/do.php?img=4826

Homework Equations


Φ=∫T.dx/G.J

The Attempt at a Solution


I have integrated torque using the formula above and reached to an answer but I'm not sure about it. my answer: 5h2 / GR4
 
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Welcome to PF;
please show your working and your reasoning.
I'm guessing the torque is not so much disturbed as distributed.
 

FAQ: Find Φ at the Point of A: Question About Torque

What is Φ in relation to torque?

Φ, also known as phi, is the symbol used to represent the angle between the position vector and the force vector in a torque equation. It is an important factor in determining the magnitude and direction of the torque on a system.

How do you calculate Φ at the point of A for torque?

To calculate Φ at the point of A for torque, you will need to use the cross product formula: Φ = sin-1 (|A x F| / (|A| * |F|)). This formula takes into account the lengths and direction of both the position vector (A) and the force vector (F).

Why is Φ important in torque calculations?

Φ is important because it represents the angle at which a force is applied to a system, which influences the magnitude and direction of the torque. It helps determine the rotational motion of an object and is essential in understanding the stability of a system.

How does the value of Φ affect the magnitude of torque?

The value of Φ directly affects the magnitude of torque. When Φ is 0 degrees or 180 degrees, the magnitude of torque is at its maximum. As Φ deviates from these angles, the magnitude of torque decreases. When Φ is 90 degrees, the torque is zero.

Can Φ be negative in torque calculations?

Yes, Φ can be negative in torque calculations. This indicates that the direction of the torque is opposite to the direction of rotation. It is important to pay attention to the sign of Φ when analyzing the rotational motion of a system.

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