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A spool whose inner core has a radius of 1.00 cm and whose end caps have a radius of 1.50 cm has a string tightly wound around the inner core. The spool is free to roll without slipping on a horizontal surface. If the string unwinds horizontally from the bottom of the core with a constant speed of 25.0 cm/s, what is the speed of the spool

Respuesta :

Answer:

v₁ = 37.5 cm / s

Explanation:

For this exercise we can use that angular and linear velocity are related

        v = w r

in the case of the spool the angular velocity for the whole system is constant,

They indicate the linear velocity v₀ = 25.0 cm / s for a radius of r₀ = 1.00 cm,

         w = v₀ /r₀

for the outside of the spool r₁ = 1.5 cm

         w = v₁ / r₁1

since the angular velocity is the same we set the two expressions equal

        [tex]\frac{v_o}{r_o} = \frac{v_1}{r_1}[/tex]

        v1 = [tex]\frac{r_1}{r_o} \ \ v_o[/tex]

let's calculate

       v₁ = [tex]\frac{1.50}{1.00} \ \ 25.0[/tex]

       v₁ = 37.5 cm / s

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