(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A student stands on a platform that is free to rotate and holds two dumbbells, each at a distance of 65 cm from his central axis. Another student gives him a push and starts the system of student, dumbbells, and platform rotating at 0.50 rev/s. The student on the platform then pulls the dumbbells in close to his chest so that they are each 22 cm from his central axis. Each dumbbell has a mass of 1.00 kg and the rotational inertia of the student, platform, and dumbbells is initially 2.40 kg•m2. Model each arm as a uniform rod of mass 3.00 kg with one end at the central axis; the length of the arm is initially 65 cm and then is reduced to 22 cm. What is his new rate of rotation?

2. Relevant equations

The initial angular momentum:

L=Iw

The moment of inertia of a rod about one end:

=1/3 m L²

The moment of inertia of the weight:

=m L²

3. The attempt at a solution

To solve this problem, use conservation of angular momentum.

The initial angular momentum is

L = I ω

I is the initial moment of inertia=2.40 kg-m²

ω is the initial angular velocity 1.15 rev / sec

converted to into radians per second= 3.14 rad/s.

****Q: Should I solve for L now?

Now we need to know the change in moment of inertia.

The moment of inertia of a rod about one end is 1/3 m L²

1/3(3kg)(.65m)^2=.4225kg*m multiplied by 2,for two arms =.845kg*m

****Q:Is the mass 3 kg? In this equation does "L" mean length or Initial angular momentum?

The moment of inertia of the weight is simply mL²

=(3kg)(.22m)^2=.1452kg*m

The difference is the change in the system moment of inertia.

>845kg*m-.1452kg*m=.6998 kg*m

I used this to compute the new moment of inertia, then use conservation of angular momentum to find the new angular velocity.

L=Iw

*********I'm stuck here because I am not getting the right answer when I solve for w or when I just solve for L. Not sure why I am not getting 1.3 rev/s,just wondering is there a calculation error or equation error?

The answer was 1.3rev/s

Thank you

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# Question regarding angular momentum and velocity.As it relates to a new rate rotation

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