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Iteru [2.4K]
3 years ago
10

A yo-yo can be thought of as a solid cylinder of mass m and radius r that has a light string wrapped around its circumference (s

ee below). One end of the string is held fixed in space. If the cylinder falls as the string unwinds without slipping, what is the acceleration of the cylinder? (Enter the magnitude. Use the following as necessary: g, m, and r.)
Physics
1 answer:
lbvjy [14]3 years ago
4 0

Answer:

6.5 m/s^2

Explanation:

The net force acting on the yo-yo is

F_net = mg-T

ma=mg-T

now T= mg-ma

net torque acting on the yo-yo is

τ_net = Iα

I= moment of inertia (= 0.5 mr^2 )

α = angular acceleration

τ_net = 0.5mr^2(a/r)

Tr= 0.5mr^2(a/r)

(mg-ma)r=0.5mr^2(a/r)

a(1/2+1)=g

a= 2g/3

a= 2×9.8/3 = 6.5 m/s^2

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