Finding Rotational Energy and Acceleration of Decending Mass

AI Thread Summary
To find the acceleration of the descending mass, apply Newton's second law to both the disk and the hanging mass, considering the moment of inertia of the disk. The moment of inertia is calculated as I_disk = (1/2)(4)(0.3)^2, resulting in 0.18 kg·m². To determine the rotational energy of the disk after 5 seconds, first calculate the angular acceleration and then use kinematic equations to find the rotational speed at that time. The rotational energy can then be derived from the formula E_rotational = (1/2)Iω², where ω is the angular speed. Understanding these relationships is crucial for solving the problem effectively.
nvallettejr
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1. A disk with radius of 0.3m and a mass of 4kg is free to rotate about an axle through its center. A cord wrapped around the circumference supports a weight with mass 5kg.

a) What is the acceleration of descending mass if it is released?

b) 5 seconds after release what is the rotational energy of the disk?



2. I disk = (1/2)MR2


3. I know that Idisk = (1/2)(4)(.3)2 is 0.18. After that I am lost.
 
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Draw two free body diagrams, one for the disk and one for the hanging mass. Write Newton's 2nd Law pertinent to each FBD.
 
Okay that sounds right I have that done but how do we get the rotational energy after 5 seconds??
 
If you know the angular acceleration, you can get the rotational speed at t = 5 s from the kinematic equations and from that the rotational energy.
 
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