Disk on a Plank Acceleration and Displacement Calculations

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SUMMARY

The discussion focuses on calculating the accelerations and displacement of a disk on a plank when a constant force is applied to the plank. The key equations involved include the moment of inertia of the disk, \( I_{disk} = \frac{1}{2}MR^2 \), and the relationship between linear acceleration and angular acceleration, \( a = \alpha R \). Participants emphasize the importance of considering both the torque and the forces acting on the system to derive the correct equations of motion. The main challenge lies in understanding how the disk rolls without slipping while the plank moves to the right.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rotational dynamics, specifically torque and moment of inertia
  • Knowledge of kinematics, particularly linear and angular relationships
  • Basic grasp of friction and its role in rolling motion
NEXT STEPS
  • Study the principles of rotational dynamics and the equations governing torque, such as \( \tau = I\alpha \)
  • Learn about the conditions for rolling without slipping and how to apply them in problems
  • Explore the concept of relative motion to understand how the disk's position changes as the plank moves
  • Practice similar problems involving forces and torques on rigid bodies to reinforce understanding
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Students in physics courses, educators teaching mechanics, and anyone interested in understanding dynamics involving rigid body motion and friction.

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disk on a plank -- HELP!

Homework Statement



a disk of mass M is sitting on a plank of length l and mass m. a constant force F is pulling the plank to the right. assuming no slipping what are the accelerations? how far to the right will the coin move before reaching the left end of the plank?

Homework Equations



Idisk=(1/2)MR^2
a=(alpha)R (no slipping parameter)
(tau)=I(alpha) (torque)
F=ma

The Attempt at a Solution



i am not really sure how to set this up. i haven't even tried the second part yet, so unless someone is really giving, i don't expect help with it. anyway, i tried treating the system as just the disk, because the plank is (presumably) sitting on the ground. i set torque = RF-Rf (force pulling and friction force) and F-f=M*a. i solved this system of equations and got nonsense. apparently I'm missing something really fundamental here. sorry i don't have any pics. i hope the description is enough.
 
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I have NO idea what your trying to say.
how far to the right will the coin move before reaching the left end of the plank?
huh?:confused:
 


as the plank is pulled, the coin rolls to the left, but the whole assembly is moving to the right. as the question is phrased, it wants to know how far to the right will the coin have moved when it falls off the plank.
 

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