Acceleration Problem due to Rotational Inertia [Exam in 9hrs]

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SUMMARY

The problem involves calculating the acceleration of a modified Atwood machine consisting of two blocks with masses m1=8kg and m2=12kg, connected by a rope over a pulley with a radius of 0.10m and a rotational inertia of I=0.040 kg-m². To solve this, one must apply Newton's Second Law for both linear and rotational motion, establishing equations for the blocks and the pulley. The correct approach includes drawing free body diagrams and using the relationship a = rα to link linear and angular acceleration. The calculated acceleration is 3.5 m/s², which is one of the provided options.

PREREQUISITES
  • Understanding of Newton's Second Law
  • Knowledge of rotational motion and torque
  • Familiarity with free body diagrams
  • Concept of rolling constraints in physics
NEXT STEPS
  • Study the application of Newton's Second Law in rotational dynamics
  • Learn how to draw and interpret free body diagrams for complex systems
  • Explore the relationship between linear and angular acceleration in rotational systems
  • Investigate the principles of modified Atwood machines in physics
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Students preparing for physics exams, educators teaching mechanics, and anyone interested in understanding dynamics involving rotational inertia and acceleration in systems with pulleys.

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[URGENT] Acceleration Problem due to Rotational Inertia [Exam in 9hrs!]

yes i know i might be late but i hope somebody can help me out with this problem because i can't figure it out. Exact word for word:

A block of mass m2= 12kg hangs from a rope. The rope wraps around a pulley and then attaches to a second block of mass m1=8kg, which sits on a frictionless table. The radius of the pulley is .10m and its rotational inertia is I=.040 kg-m2. What is the acceleration of the blocks when they are released.

here is how it looks:

http://spiff.rit.edu/classes/phys311/workshops/w5b/level_atwood/cart_and_weight.gif

a modified atwood machine.
 
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You essentially need to draw 3 free body diagrams. Use Newton's Second Law to set up the equations for the two blocks, and Newton's Second Law for rotational motion, [tex]\Sigma \tau = I \alpha[/tex] to set up an equation for the net torque on the massive pulley. Also note, you'll want to use the rolling constraint [tex]a = r \alpha[/tex] to get the angular acceleration in terms of "a." Does this help?
 
sort of i was using
a=F/m
F=m2g->12*9.80=118
m=12kg + 8kg
a=5.9

but its not one of the choices which are:
a. 3.5
b. 3.9
c. 2.5
d. less than 2.5
e. cannot be determined
 

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