Moment of Inertia - Swinging arms

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SUMMARY

The discussion centers on the calculations related to the moment of inertia and angular motion, specifically addressing the relationship between torque, angular acceleration, and tangential velocity. The correct formula for torque is established as τ = Iα, where α represents angular acceleration, contrasting with the incorrect use of τ = Iw. The participant also clarifies that the tangential velocity is derived from the equation a = αr, rather than v = wr as initially stated. The calculations indicate that a speed of 340 (Mach 1) can be achieved in 128 seconds under the given conditions.

PREREQUISITES
  • Understanding of angular motion concepts, including moment of inertia (I) and angular acceleration (α).
  • Familiarity with torque calculations in rotational dynamics.
  • Knowledge of the relationship between linear and angular velocity.
  • Basic grasp of kinematic equations in rotational systems.
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  • Study the derivation and applications of the torque equation τ = Iα in various physical systems.
  • Learn about the relationship between angular displacement and tangential velocity in rotational motion.
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elemis
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momi_12.jpe


My workings are below :

ImageUploadedByPhysics Forums1366692390.758620.jpg


Following the calculation of w I use v=wr where r= 3 and calculate the tangential velocity.

It's then easy to see that a speed of 340 (Mach 1) will be attained in 128 s

Is this correct ?
 
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In your handwritten working, you've written omega instead of omega-dot, but otherwise it all looks correct.
 
haruspex said:
In your handwritten working, you've written omega instead of omega-dot, but otherwise it all looks correct.

I don't understand you. Torque = Iw , correct ?
 
elemis said:
I don't understand you. Torque = Iw , correct ?

No, it is

τ = Iα

where α is the angular acceleration
 
Last edited:
hms.tech said:
No, it is

τ = Iα

where α is the angular acceleration
... and although the OP says "I use v=wr ", what has actually been used is a = αr.
 

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