Rotational Inertia and Angular Momentum

AI Thread Summary
The discussion revolves around calculating the angular momentum of a disk with a rotational inertia of 8.38 kg·m² under a time-dependent torque. The initial angular momentum at t = 1.00 s is given as 6.57 kg·m²/s. The user attempts to derive the angular momentum at t = 3.00 s using the relationship between torque and angular momentum but arrives at an incorrect value. They highlight the importance of correctly integrating the torque function and mention a common mistake related to integration. The thread emphasizes the need for careful application of calculus in solving physics problems.
ScreamingIntoTheVoid

Homework Statement


A disk with a rotational inertia of 8.38 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.03 + 1.01t) N · m. At time t = 1.00 s, its angular momentum is 6.57 kg·m2/s. What is its angular momentum at t = 3.00 s?

Homework Equations


dL/dt= T L=Iw

The Attempt at a Solution


dL/dt=T (my symbol for touque) -> L=5.03t+1.01t^2+C --> 5.03 (1)+ 1.01(1)^2+C= 6.57 -->C=0.53

L=5.03(3)+ 1.01(3)^2 +0.53 --> 24.71 kg*m/s^2

Apparently that's wrong... Help?
 
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For the sake of any suffering physics student that comes upon this, remember as I did not the integral of x= (x^2)/2 and you should be able to solve this.
 
So, you solved this problem, right?
 

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