Solving Rotational Dynamics Problems with Torques & Acceleration

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SUMMARY

The discussion focuses on solving a rotational dynamics problem involving a wheel with a radius of 2 m, mass of 53 kg, and a moment of inertia calculated as (3/4)(53 kg)(2 m)^2. The problem requires determining the velocity of a falling mass of 106 kg at a distance of 28 m and the tension in the supporting string. The user correctly calculated the acceleration as 7.0189189 m/s², leading to a velocity of 19.83 m/s at point B. However, the tension calculation yielded an incorrect result of 294.79 N, prompting a request for further assistance in resolving the discrepancy.

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  • Understanding of rotational dynamics and torque equations
  • Familiarity with moment of inertia calculations
  • Knowledge of kinematic equations for linear motion
  • Basic principles of Newton's second law applied to rotational systems
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Hello,
I have a problem dealing with torques and acceleration. I am sure I solved it right but when submitting the answers, I get the response "Incorrect" :cry:

The problem:

A wheel of radius 2 m, mass 53 kg, and moment of inertia (3/4) (53 kg) (2m)^2 about the center of mass is mounted on a frictionless horizontal axle.
(g = 9.8). A light cord wrapped around the wheel supports an object of mass 106 kg. The weight is released from rest at the level of A and falls a distance h, past level B (AB=28 m). a) Find the velocity as it passes B b) Determine the tension of the string.

I set up everything.

Torque = I* alpha = T*R since alpha = a/R and we know I, conclusion is T=42*a

Then: T=m(g - a): putting T from above, I got a=7.0189189 m/s^2
To find V as the mass passes point B: Vf^2 = 2*a*28m ---> and v at B = 19.83 m/s. This was OK

For b) I used T=m(g-a), since I know a = 7.0189189m/s^2 , I substituted it at the equation and I got T= 294.79 N but this is not the right answer.

Maybe I can use I*alpha = T*R and from that get T because everything is known, but I am not sure. Any suggestions?
 
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Can anyone help?
 
For part a)
F=mg
Torque=mgr
mgr=I(alpha)
28=r(theta)
Wf^2=Wi^2+2(alpha)(theta)
Vf=r(Wf)

For part b)
a=R(alpha)
T=m(g-a)

Do these things help?
 

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