Mass of cylinder using ang.velocity

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The discussion focuses on calculating the mass of a solid uniform cylinder using angular velocity and energy conservation principles. The system involves a 3 kg stone tied to a string wrapped around the cylinder, which falls 2.5 m and reaches a speed of 3.5 m/s. The user correctly identifies the need to apply the rotational inertia formula I = 1/2 Mr^2 and the kinetic energy equation Kf = 1/2mv^2 + 1/2Iw^2. They derive angular velocity using the relationship v = rw, resulting in an angular velocity of 9.3 rad/s. The user expresses uncertainty about solving for the unknowns in the kinetic energy equation and seeks confirmation on their approach.
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A light string is wrapped around the outer rim of a solid uniform cylinder of radius .375m that can rotate without friction about an axle through its center. A 3.00 kg stone is tied to the free end of the string When the system is released from rest, you determine that the stone reaches a speed of 3.50 m/s after having fallen 2.50m .
What is the mass of the cylinder?

Ive solved for:
F=M*a
3kg*9.8=29N
29N*2.5m=73.5J

i know its a solid cylinder so I=1/2 Mr^2 so i need to solve for the inertia. from here i got stuck i know i have to use

Kf=1/2mv^2+1/2Iw^2 i don't know where to go from here. do i solve for the angular velocity(w)? or Inertia?

i know v=rw so would w=v/r i could use 3.5m/s/.375m to get 9.3rad/s?
 
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anyone know if I am doing this one rite?
 
i used the Ki + Ui=Kf + Uf

Ki=0
Ui=mgy=73.5J
Kf=1/2mv^2+1/2Iw^2
Uf=0

i got
73.5=1/2Iw^2+18.375 so

1/2(I)w^2=55.125J

im stuck on Kf where i have to solve for the two unknowns I* w* i used v=rw to solve for w is that correct?
 
Last edited:
got it
 

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