How does tension affect the motion of a hanging block on a rotating disk?

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SUMMARY

The discussion centers on the dynamics of a hanging block on a rotating disk, specifically addressing the tension in the cord and its effect on motion. The uniform disk has a mass of 2.5 kg and a radius of 20 cm, while the hanging block has a mass of 1.2 kg. Key equations include T – mg = ma and torque = I α, with torque calculated as -RT due to the chosen direction of tension. The negative sign arises from the convention of positive direction being upwards, while tension acts downwards.

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  • Understanding of Newton's second law of motion
  • Familiarity with rotational dynamics and torque
  • Knowledge of moment of inertia calculations
  • Basic grasp of vector direction conventions in physics
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  • Learn about moment of inertia for various shapes, particularly disks
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Homework Statement


This figure shows a uniform disk, with mass M = 2.5 kg
and radius R = 20 cm, mounted on a fixed horizontal axle.
A block with mass m = 1.2 kg hangs from a massless cord
that is wrapped around the rim of the disk.

Sample problem 10-8 (has picture diagram and detailed solution): http://astro1.panet.utoledo.edu/~mheben/PHYS_2130/Chapter11-1_mh.pdf

Homework Equations


T – mg = ma
torque = I α
-RT ? = (1/2)MR^2 α
a = a(subscript t) = α R

The Attempt at a Solution


I understand how to do the problem but what I don't understand is how they got -RT. Torque is FrSin(theta) and the sin of 90 degrees is 1 not -1 so I would really appreciate any insight on how they got -RT.
 
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Well, it looks like positive direction is chosen to be up and vector T is pointing down so...
 
lep11 said:
Well, it looks like positive direction is chosen to be up and vector T is pointing down so...
Ok thanks
 

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