2/5 String is comtart tore , suh that tre te tho ot et doit mot mno e up cr down

Question

2/5 String is comtart tore , suh that tre te tho ot et doit mot mno e up cr down but the ob ect spin faster and faster (see figure below). This is like a yoyo: nothing but the touches the object. When your hand is a height yo 0.25 m above the floor, the object has an angular speed 13 rad/'s. Whan your hand has risen to a floor, what is the angular speed of the object? around an object of mass 1.6 kg and moment of inertia 0.0018 kg·m" the density of th. object is not uniform with your hand you pull the string straight up with some M.I DOLL

Explanation / Answer

given mass M = 1.6 kg
moment of inertia I = 0.0018 kgm^2
force applied to the string = F
at yo = 0.25, wo = 13 rad/s
y = 0.34 m, w = ?

so let radius of the object be r
then torque = Fr
angular acceleration, alpha = Fr/I

also, from force balance
F = Mg

now, work done by torque on the object = Fr * (y - yo)/r = F(y - yo)
change in KE = 0.5I(w^2 - wo^2)
hence
form work energy theorem
F(y - yo) = 0.5*I*(w^2 - wo^2)
1.6*9.81(0.34 - 0.25) = 0.5*0.0018*(w^2 - 13^2)
w = 41.696 rad/s = final angular speed

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