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

In summary, we have a thin disc of mass m resting on a rough horizontal surface. The disc has a centre of mass offset from the centre by h and a radius r. The disc is originally at rest and then released, with no slip occurring between the disc and the surface. The equations of motion for the disc can be written as F = ma, where F is the net force acting on the disc and a is the acceleration. The disc has two degrees of freedom, corresponding to its motion in the x and y directions. To solve the equations of motion, we need to consider the kinematic constraints, which can be written as h = r sin(theta) and v = r omega, where theta is the angle between the horizontal surface
  • #1
confused89
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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
 
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  • #2
confused89 said:
centre of mass offset from centre by h (horizontally right in diagram)

please provide a diagram to make it clear.
 

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

1. What is an equation of motion?

An equation of motion is a mathematical representation of the motion of an object over time. It describes the relationship between an object's position, velocity, and acceleration as it moves through space.

2. How do you derive equations of motion for a disc?

The equations of motion for a disc can be derived using Newton's laws of motion and the principles of rotational motion. By considering the forces acting on the disc and its rotational inertia, we can develop equations that describe its motion.

3. What are the variables in equations of motion for a disc?

The variables in equations of motion for a disc include the disc's position, velocity, and acceleration, as well as its mass, radius, and moment of inertia. Other factors such as external forces and friction may also be included in the equations.

4. Can equations of motion be used to predict the future motion of a disc?

Yes, equations of motion can be used to predict the future motion of a disc. By plugging in the initial conditions and solving the equations, we can determine the disc's position, velocity, and acceleration at any point in time.

5. Are there any real-world applications of equations of motion for a disc?

Yes, there are many real-world applications of equations of motion for a disc. Some examples include analyzing the motion of spinning objects such as frisbees or wheels, designing efficient rotating machinery, and predicting the trajectory of objects in orbit.

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