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Triathlete
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Homework Statement
4) In order to determine the moment of inertia I of a rotating platform, a string is wrapped
around a spool of radius r = 2.0 cm beneath the platform. The string is then fed over a
pulley with a hanging mass attached to its end. The hanging mass is then released from rest, and its linear acceleration is measured.
A.) If the hanging mass is M = 100 g, and its linear acceleration is a = 2.5 m/s2, what is the moment of inertia I of the rotating platform?
B.) Using the same rotating platform as in problem 1, a ball of mass m = 50 g is launched
into the catcher on top of the platform. After the ball is caught by the catcher, the angular velocity of the system is ω = 2.2 rad/s. If the catcher is R = 20 cm away from the axis of rotation of the platform, what is the linear velocity v of the ball before it is caught?
Homework Equations
FT = M(g-a)
α = a/r
I = (rFT)/α
vo = ([itex]\omega[/itex]r2M(g-a))/amR
The Attempt at a Solution
For part a, I used the first two equations to solve for the tension force and angular acceleration, then plugged the values into the third equation to solve for inertia. The answer I got was 1.17x10-4 kgm2 (If you could verify this, that would be great!
For part b I am not sure where to begin, because there are too many unknowns. I can't figure out a way to combine any of the equations to solve for any of the unknowns either.
Thanks in advance for your help!