A yoyou is released from res. With the information given below. what is the line

Question

A yoyou is released from res. With the information given below. what is the linear speed of the yo-yo after it has dropped through a height of h = 0.50m?

Yo-Yo man releases a yo-yo from rest and allows it to drop, as he keeps the top end of the string stationary, as shown in the image. The mass of the yo-yo is 0.056 kg, its moment of inertia is 2.9 x 10-5 kg . m2, and the radius, r of the axle the string wraps around is 0.0064 m. What is the linear speed, v, of the yo-yo after it has dropped through a height h = 0.50 m.

Explanation / Answer

By Conservation of Energy

KE_Linear +KE_rotational =U_gravitational

(1/2)mV^2 +(1/2)IW^2 =mgh

since W=V/r

(1/2)mV^2+(1/2)I*(V/r)^2 =mgh

(1/2)*V^2 *[m+I/r^2] =mgh

=>V^2 =mgh/(1/2)*[m+(I/r^2)]

V^2 =(0.056*9.8*0.5/(1/2)*[0.056+2.9*10^-5/0.0064^2]

V=0.8475 m/s

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