Rotational Motion-Up an Incline

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SUMMARY

The discussion focuses on the dynamics of a solid sphere, thin hoop, and solid disk rolling down an incline and subsequently rolling up another incline. The key takeaway is that while the solid sphere has the highest kinetic energy (KE) at the bottom of the incline, the potential energy (PE) and kinetic energy at the start of the upward motion are critical in determining which object travels the furthest. The correct analysis reveals that the initial conditions, rather than just the KE at the bottom, dictate the distance traveled up the incline.

PREREQUISITES
  • Understanding of rotational motion and energy conservation principles
  • Familiarity with the equations for kinetic energy of different shapes (solid sphere, thin hoop, solid disk)
  • Knowledge of potential energy in gravitational fields
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of energy conservation in rotational motion
  • Learn about the moment of inertia for various geometric shapes
  • Explore the effects of friction on rolling motion
  • Investigate the relationship between kinetic energy and potential energy in inclined planes
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of rotational motion and energy dynamics in inclined planes.

abspeers
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Homework Statement



A solid sphere (S), a thin hoop (H), and a solid disk (D),
all with the same radius, are allowed to roll down an
inclined plane without slipping. At the bottom, they run into another inclined plane and begin rolling upwards. Which will travel the furthest up the inclined plane, neglecting all frictional forces?

Thin Hoop KE=1/2mv^2 + 1/2(MR^2)w^2

Solid Sphere KE=1/2mv^2 + 1/2(2/5MR^2)w^2

Solid Disk KE=1/2mv^2 + 1/2(1/2MR^2)w^2

Homework Equations



1/2mv^2 + 1/2Iw^2 = mgh

The Attempt at a Solution



A previous question had asked which reaches the bottom first and I had found that to be the sphere, followed by the disk, and finally the thin hoop. I suspect that the sphere would travel the furthest up the incline because it has the greatest KE at the bottom of the first incline, but I am unsure if this assumption is correct.

Thank you for the help!
 
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Welcome to PF!

Hi abspeers! Welcome to PF! :smile:
abspeers said:
… I suspect that the sphere would travel the furthest up the incline because it has the greatest KE at the bottom of the first incline, but I am unsure if this assumption is correct.

You're right, it's not correct …

never mind the KE at the bottom, its the KE and PE at the start that matters, isn't it? :wink:
 

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