Finding the Height of a Nail for a Rolling Cylinder without Slipping

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SUMMARY

The discussion centers on calculating the height of a nail (h) above the floor for a rolling cylinder to reverse direction without slipping after colliding with the nail. The cylinder has a radius (R) and a moment of inertia (I = MR²/2). Key equations include conservation of linear momentum and angular momentum, leading to the conclusion that h = 3R/2 for the cylinder to roll back without slipping. The analysis emphasizes the importance of torque and the role of lateral forces applied by the nail during the collision.

PREREQUISITES
  • Understanding of rotational dynamics and torque
  • Familiarity with conservation laws in physics (linear and angular momentum)
  • Knowledge of moment of inertia (I = MR²/2) for rigid bodies
  • Basic principles of friction and rolling motion
NEXT STEPS
  • Study the principles of conservation of angular momentum in collisions
  • Learn about the effects of torque on rolling objects
  • Explore the relationship between linear and angular velocities in rolling motion
  • Investigate the role of friction in preventing slipping during rolling
USEFUL FOR

Students and educators in physics, mechanical engineers, and anyone interested in the dynamics of rolling motion and collision analysis.

  • #31
tiny-tim said:
(I take it you mean a stationary wheel)

It depends where you apply the force.

If the point of application is the centre of the wheel (or if the line of application passes through the centre), then I agree. But if the point of application is off-centre, then the wheel will accelerate and will start to turn.

:

yes that was what i meant. The difference being that if there was friction, then the wheel would turn.

again, i thought that slipping means that something doesn't have enough grip. And with grip you have friction. So in order to see when the wheel would slip, you got to have friction for that./
 
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  • #32
Oerg said:
yes that was what i meant. The difference being that if there was friction, then the wheel would turn.

You're missing my point, that even that if there is no friction, then the wheel can still turn:
tiny-tim said:
But if the point of application is off-centre, then the wheel will accelerate and will start to turn.

You agree?

Then, if you judge the point of application right, the velocity and the turn may match, and there will be no slipping - even on ice! :smile:

Do you agree? :smile:
 

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