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Haveagoodday
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1. Homework Statement
A yo-yo roughly speaking consists of two round, uniform discs, sandwiched
around a third smaller disc. A string is wound around the middle disc, and so
the yo-yo may roll up and down as the string winds and unwinds. Consider
such a yo-yo, with the two bigger discs having radius R = 4.00 cm and mass
M = 30.0 g each; and the smaller disc in the middle having radius r = 0.700
cm and mass m = 5.00 g. The string is taken to be massless, and infinitely
thin.
a) What is the total moment of inertia of the yo-yo, around an axis going
through the centre of the discs? Indicate both the algebraic expression and
a number.
b) The end of the string is now fastened to something at a fixed position
(like a finger), and the yo-yo is let drop towards the floor. Identify the forces
acting on the yo-yo, and for each, indicate whether they provide torque, work,
impulse and/or acceleration to the yo-yo.
c) What is the acceleration of the yo-yo downwards; what is its angular
acceleration? How large is the string force?
d) How big a fraction of the total kinetic energy goes into the rotating motion?
The Attempt at a Solution
Can somebody check my solutions?
a)
ΣI= 1/2mr^2 + MR^2=4.812 kg*m^2
b)
There are forces like force of gravity and string force
gravity provides Work and acceleration
string provides torque and impulse
c) a=g= 9.80 m/s^2
Fg=2Mg=0.588 N
Fg=mg=0.049 N
τ=RFg=0.02352
τ=rFg=3.43*10^-4
α=Στ/ΣI=5.6 rad/s^2
Fs=mg/1-(mR^2/ΣI)= 0.388 N
d) haven't solved this one yet, does anybody have an idea for how to solve this one?
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