A Yo-Yo of mass m has an axle of radius b and a spool of radius R . Its moment of inertia about the center can be taken to be I=(1/2)mR2 and the thickness of the string can be neglected. The Yo-Yo is released from rest. You will need to assume that the center of mass of the Yo-Yo descends vertically, and that the string is vertical as it unwinds.
(a) What is magnitude of the tension in the cord as the Yo-Yo descends? Express your answer in terms of m, b, R and acceleration due to gravity g (enter m for m, b for b, R for R and g for g).
T=
m⋅g1+(2⋅b2R2)
(b) Find the angular speed of the Yo-Yo when it reaches the bottom of the string, when a length l of the string has unwound. Express your answer in terms of m, b, R, l and acceleration due to gravity g (enter m for m, b for b, R for R and g for g).
ωf=
(4⋅g⋅l2⋅b2+R2)12
(c) Find the magnitude of the tension in the string as the Yo-Yo reverses its direction at the bottom of its descent (see figure below).
Express your answer in terms of m, b, R, l and acceleration due to gravity g (enter m for m, b for b, R for R, g for g and pi for π).
Tr=
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(c) Find the magnitude of the tension in the string as the Yo-Yo reverses its direction at the bottom of its descent.
Express your answer in terms of m, b, R, l and acceleration due to gravity g (enter m for m, b for b, R for R, g for g and pi for π).
Tr=
ùf=sqrt((2*l)/(1/2*m*R^2)*(m*g)/(1+(m*b^2)/(1/2*m*R^2)))
Ôr=m*g+(2*m*b)/pi*((2*l)/(1/2*m*R^2)*(m*g)/(1+(m*b^2)/(1/2*m*R^2)))
1 answer