Equations about this torsional spring and movements

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In summary, the conversation discusses the use of the second Newton law to analyze the force on m1 and m2 in a system where gravity force is not considered and m2 can only move vertically. The system is linked by a torsion spring and the equation related to the spring is written with the positions of m1 and m2. The first question is about the inclusion of the dθ/dt factor in the frictional term and the second question asks for an equation representing the motion in two directions. It is noted that the acceleration of m1 should also be affected by m2's acceleration. Additionally, the conversation mentions that for the system, the only external force parallel to F is F itself, indicating that the mass center of the
  • #1
Raymond1227
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Here I want to analyse the force imposed on m1 and m2 while using the second Newton law.
The top view of the system shows like below, thus gravity force is not considered, m2 can only move along the vertical line, and one torsion spring link m1 and m2. The length between m1 and spring is L, length between m2 and spring is negligible. The I have written the equation related to spring. where x1 and x2 is the position of m1 and m2 respectively. F is the force on m2.

My question is how should I write a equation related to x2 and force F. And equation about the whole system. Thank you.

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  • #2
Two questions...
Why the dθ/dt factor in the frictional term? Isn't torsional friction just a constant, so long as the motion is in one direction?
If m2 is accelerating, shouldn't that contribute to m1's acceleration? I.e., shouldn't the right hand side be ##m_1(\ddot x_1-\ddot x_2)L##?
 
  • #3
Thank you for your reply. The m2 can move upwards and downwards, in two direction. The second question is what I concerned. I don't know how to write the equation to represent this.
 
  • #4
Raymond1227 said:
Thank you for your reply. The m2 can move upwards and downwards, in two direction. The second question is what I concerned. I don't know how to write the equation to represent this.
For the system consisting of the two masses and everything in between, the only external force parallel to F is F itself. What does that tell you about acceleration of the mass centre of the system?
 

Related to Equations about this torsional spring and movements

1. What is a torsional spring?

A torsional spring is a type of spring that works by twisting or rotating along its axis. It is usually made from a material that can be easily deformed, such as metal or plastic. When a force is applied to the spring, it produces a torque or rotational force that is proportional to the amount of twist.

2. How do you calculate the spring constant of a torsional spring?

The spring constant of a torsional spring can be calculated by dividing the torque applied to the spring by the angle of twist. This value is also known as the spring's stiffness and is measured in units of torque per angle, such as Nm/° or ft-lb/°.

3. What is the relationship between the angle of twist and the applied torque in a torsional spring?

The angle of twist and the applied torque in a torsional spring have a linear relationship. This means that the more torque is applied to the spring, the greater the angle of twist will be. This relationship is described by the equation T = kθ, where T is the torque, k is the spring constant, and θ is the angle of twist.

4. How does the stiffness of a torsional spring affect its movement?

The stiffness of a torsional spring directly affects its movement. A stiffer spring will require more torque to produce a certain amount of twist, resulting in a smaller angle of twist. On the other hand, a less stiff spring will require less torque and produce a larger angle of twist. This relationship is also known as Hooke's law.

5. Can a torsional spring have different stiffness values for different angles of twist?

Yes, a torsional spring can have different stiffness values for different angles of twist. This is due to the material properties of the spring, such as its modulus of elasticity, which can vary at different levels of deformation. However, for small angles of twist, the stiffness of the spring is usually considered to be constant.

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