Tension of rod connecting two cylinders

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SUMMARY

The discussion focuses on calculating the tension in a rod connecting two cylinders (one hollow and one solid) rolling down an inclined plane without skidding. The key variables include mass (M), incline angle (α), and gravitational acceleration (g). Participants clarify that tension arises from the stretching of the rod due to the differing moments of inertia of the cylinders, which affects their acceleration. The final equations derived indicate that the ratio of torque to radius (T/R) equals 3/2 * mg sin(α), providing a definitive formula for tension in this system.

PREREQUISITES
  • Understanding of Newton's second law of motion for translational and rotational dynamics.
  • Familiarity with concepts of moment of inertia for solid and hollow cylinders.
  • Knowledge of static friction and its role in rolling motion.
  • Basic trigonometry to analyze forces on an inclined plane.
NEXT STEPS
  • Study the derivation of moment of inertia for various shapes, focusing on hollow and solid cylinders.
  • Learn about the principles of static friction and its impact on rolling motion.
  • Explore the application of Newton's laws in rotational dynamics, particularly in multi-body systems.
  • Investigate the relationship between torque and angular acceleration in rigid body dynamics.
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Students studying physics, particularly those focusing on mechanics, as well as educators and professionals involved in teaching or applying concepts of dynamics and rotational motion.

  • #31
zemaitistrys said:
How would you define the quantity required to find in the problem then? Torsion sure ain't measured in Newtons.
No, it's a torque, in Newton metres.
 
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  • #32
haruspex said:
No, it's a torque, in Newton metres.

It was specified to find a force, the distinction is quite clear in the language the problem is written in.
 
  • #33
zemaitistrys said:
It was specified to find a force, the distinction is quite clear in the language the problem is written in.
Then I see no way to answer the question.

Edit: maybe I do...
The original post said, specifically, a tension. Let's ignore that, and also suppose the rod acts as a smooth axle for each cylinder, so cannot exert an axial torque. For simplicity, suppose it contacts each cylinder only at two bearings, one at each end of the cylinder.
There will be four forces on the rod from these bearings. Each is parallel to the plane and normal to the rod.
The combination of the two forces from one cylinder can be thought of as one force plus a torque normal to the plane. If we ignore the torque, we could consider this net force as the force the question is after.
 
Last edited:

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