Should I consider Linear Kinetic Energy in this Equation

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SUMMARY

The discussion centers on the necessity of considering Linear Kinetic Energy when calculating Torque for a rolling disc on a non-slope plane. The derived equations for Torque include both linear and angular components, specifically τ=d(½Mv²+½Iω²)/dθ and τ=(I+Mr²)α. It is established that the total energy must account for potential, kinetic, and rotational energy, emphasizing the importance of the center of rotation and the moment of inertia. The consensus is that both Linear and Angular Kinetic Energy should be included in the calculations.

PREREQUISITES
  • Understanding of Torque and its derivation
  • Knowledge of Kinetic Energy, including Linear and Angular components
  • Familiarity with the concept of Moment of Inertia
  • Basic principles of rotational dynamics
NEXT STEPS
  • Study the derivation of Torque in rotational systems
  • Learn about the Moment of Inertia for various shapes, particularly discs
  • Explore the relationship between Linear and Angular Kinetic Energy
  • Investigate the effects of potential energy in rolling motion scenarios
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in dynamics and rotational motion analysis will benefit from this discussion.

Vichakron
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Sorry If the thread name confuse you.
I want to know if I want to find the Torque from deriving Kinetic Energy and the system has Object the Rotate and the rotating cause linear motion(v).
Let's say it a Rolling Disc on the non-slope plane which has angular velocity ω and that ω cause it to move forward at velocity v.

Should I consider Linear Kinetic Energy? which I think will result,
τ=d(½Mv2+½Iω2)/dθ
τ=(I+Mr2)α
or shouldn't I?
τ=Iα.

Sorry if my question wasn't clear or my English was confusing.
Anyways, Thanks in advance.
 
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Welcome to PF.
A rolling disc has potential, kinetic and rotational energy. You must account for the total.
For a disc it is the centre of rotation that is important. The moment of inertia is a function of mass and section.
You must add the angular KE about the centre to the linear KE of the centre.
Where the height of the centre changes you must also include PE.
 
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Baluncore said:
Welcome to PF.
A rolling disc has potential, kinetic and rotational energy. You must account for the total.
For a disc it is the centre of rotation that is important. The moment of inertia is a function of mass and section.
You must add the angular KE about the centre to the linear KE of the centre.
Where the height of the centre changes you must also include PE.

Thank you so much for the answer.
 

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