What Are the Equations of Motion for a Disc on a Rough Surface?

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SUMMARY

The discussion focuses on deriving the equations of motion for a thin disc of mass m with its center of mass offset by a distance h on a rough horizontal surface. The frictional force acting on the disc is defined by the equation F = ((m^2)rh(g-h(α)))/(I+mr^2), where I represents the moment of inertia of the disc about the axis through its center of mass. The problem also requires identifying the degrees of freedom and formulating the necessary kinematic constraint equations to solve the equations of motion. A diagram is suggested to enhance understanding of the setup.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the concept of moment of inertia
  • Knowledge of kinematic constraints in rigid body dynamics
  • Basic principles of friction in mechanics
NEXT STEPS
  • Study the derivation of the moment of inertia for various shapes, focusing on the thin disc
  • Learn about the equations of motion for rigid bodies with constraints
  • Explore the role of friction in rotational motion and its impact on dynamics
  • Review kinematic constraint equations and their applications in mechanics
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Students in physics or engineering courses, particularly those studying mechanics, as well as educators preparing materials on rigid body dynamics and frictional forces.

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Homework Statement



A thin disc if mass m, centre of mass offset from centre by h (horizontally right in diagram), and radius r rests on a rough horizonal surface. It is originally at rest and then released. No slip occurs between disc and horizontal surface.

Write the equations of motions of the disc.
How many degrees of freedom?
Write the kinematic constraint equations required to solve the equations of motion.

Show that frictional force acting on the disc is F=((m^2)rh(g-h(alpha)))/(I+mr^2)
where I = moment of inertia of disc about axis through the centre of mass, normal to the disc.

Homework Equations


The Attempt at a Solution



just not really sure where to start at all.

its for an exam not homework but I really need help. thanks
 
Last edited:
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confused89 said:
centre of mass offset from centre by h (horizontally right in diagram)

please provide a diagram to make it clear.
 

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