Analyzing the Vertical Acceleration of a Yo-yo Using Moment of Inertia

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SUMMARY

The discussion focuses on calculating the vertical acceleration of a yo-yo by utilizing its moment of inertia. The total moment of inertia for the yo-yo is established as ##I_{\text{tot}}=\frac12mr^2+MR^2##, where ##m## and ##M## represent the masses of the smaller and larger cylinders, respectively. Participants emphasize the importance of incorporating gravitational acceleration into the equations of motion, specifically ##\sum F = ma## and ##\sum \tau = I \alpha##. A free body diagram is recommended to visualize the forces and torques acting on the yo-yo.

PREREQUISITES
  • Understanding of moment of inertia, particularly for solid cylinders
  • Familiarity with Newton's laws of motion, specifically force and torque equations
  • Basic knowledge of gravitational acceleration and its effects on motion
  • Ability to create and interpret free body diagrams
NEXT STEPS
  • Study the derivation of moment of inertia for composite objects
  • Learn how to apply Newton's second law in rotational dynamics
  • Explore the concept of torque and its relationship with angular acceleration
  • Practice drawing and analyzing free body diagrams for various mechanical systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators seeking to enhance their teaching methods in these areas.

Cepterus
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Homework Statement


A yo-yo consists of two cylinders with radius ##R##, mass ##M## and height ##H## connected by a smaller cylinder of radius ##r##, mass ##m## and height ##h##.
Unbenannt.png

Determine the yo-yo's acceleration in ##z##-direction, using its moment of inertia.

Homework Equations


Moment of inertia of a solid cylinder: ##I=\frac12mr^2##

The Attempt at a Solution


The yo-yo's total moment of inertia is ##I_{\text{tot}}=\frac12mr^2+MR^2##, using the formula for solid cylinders. However, I don't know how to proceed from here.
 
Last edited:
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Free body diagram.
##\sum F = ma##.
##\sum \tau = I \alpha##.
 
Hi Cep,

Could gravitational acceleration appear somewhere ?
 
BvU said:
Could gravitational acceleration appear somewhere ?
I guess so. The acceleration probably consists of both gravitational acceleration downwards and the acceleration upwards caused by the "user" of the yo-yo.
Is that what you mean?
 
Yes. Make a sketch where the driving force acts and how it results in a torque.
 

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