Does velocity from rotational Ek add to a total velocity of a body?

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SUMMARY

The discussion centers on the calculation of the final velocity of a ball rolling off an inclined roof, emphasizing the importance of both translational and rotational kinetic energy (KE). The correct approach to determine the initial velocity involves applying the conservation of energy principle, which incorporates both EK(transl) and EK(rot). While the focus may be on the translational motion of the center of mass, neglecting the rotational component leads to an incomplete analysis. Thus, both forms of kinetic energy must be considered for accurate results.

PREREQUISITES
  • Understanding of conservation of energy principles in physics
  • Familiarity with kinetic energy equations: EK(transl) and EK(rot)
  • Basic knowledge of rotational motion and its effects on translational motion
  • Ability to analyze motion on inclined planes
NEXT STEPS
  • Study the conservation of energy in mechanical systems
  • Learn about the equations for translational and rotational kinetic energy
  • Explore examples of motion on inclined planes in physics textbooks
  • Investigate the relationship between rotational inertia and translational motion
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of rolling objects and energy conservation principles.

rammer
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If we have a ball rolling down from inclined roof that has bottom part at certain height about the ground. I want to know where does the ball land after it leaves the roof. So at this point potential energy is transferred to kinetic (rotational + translational).

My question is: What is the expression I derive an initial velocity from? Is it EK(transl) or EK(transl)+EK(rot)?

I think it should be only EK(transl), because I'm interested only in motion of a centre of mass, right?
BUT, exercises in my book always counts with EK(rot), so I'm pretty confused.

Can you please make it little more clear to me??
 
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To find the final velocity of the ball as it leaves the roof you must use conservation of energy. That includes all forms of mechanical energy, which in this case is both rotational and translational KE.

Even though all you care about is the translational speed of the ball, in order to correctly find that speed you must use conservation of energy properly.
 
thank you
 

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