Angular Velocity on a circular platform

[Naldo6]

A large horizontal circular platform (M=120.1 kg, r=3.45 m) rotates about a frictionless vertical axle. A student (m=73.3 kg) walks slowly from the rim of the platform toward the center. The angular velocity w of the system is 3.9 rad/s when the student is at the rim. Find w (in rad/s) when the student is 2.47 m from the center.

Does the angular velocity w is not the same everywhere in the circular platform?...
i put 3.9 rad/s and the answer was wrong

 

[Naldo6]

i use de I1W1=I2W2

if I= (1/2)Mr^2 then:

(1/2)MR1^2W1=(1/2)MR2^2W2

finding out for... W2= [(R1^2) / (R2^2)]* W1

W2= [(3.45^2)/(2.47^2)]*(3.9)
W2= 7.61 rad/s

the answer is wrongs...Can anyone help me please...

 

[alphysicist]

Hi Naldo6,

i use de I1W1=I2W2

if I= (1/2)Mr^2 then:

(1/2)MR1^2W1=(1/2)MR2^2W2

This equation is not correct. The angular momentum is not conserved for the student alone or the platform alone; it is conserved for the combination (platform+student). This means that the rotational inertia I has to be that of the combination (platform+ student).

So for your equation I1W1=I2W2 :

I1 = (initial I for platform) + (initial I for student)

and a similar quantity for I2. Do you get the right answer?

 

[Naldo6]

ty it gives me the correct answer with ur suggestion...