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dentulousfing
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Homework Statement
A rotating disk of 2.50m in diameter serves tu connect a counter weight to a mass through a massless rope. The rope does not slip on the disk so, there is no friction on the rim. What angular velocity in rpm must the disk turn to raise the elevator at 25.0 m/s?
Homework Equations
v=r*omega
a(rad)=omega^2*r
The Attempt at a Solution
I am confused here.
since the linear velocity of the rope is constant, its linear acceleration should be zero, and every point on the rope should have the same velocity. Becasue the radius of the rim is constant, the angular velocity should be zero and angular acceleration as well.
a(tan)=r*alpha
alpha=0
a(tan)=0
because the tangential acceleration is zero, then the acceleration vector should have a radial component only: a(rad)=omega^2*r
I could factor out omega from the equation and obtain:
omega=square root of a(rad)/r.. but I don't have the radial component of the acceleration...
should I just use the equation v=omega*r, and factor out omega from it?
Just wondering, if I were given the tension on the rope, caused by the weight of the mass connected to it, or a given displacement with this constant pulling force by the rope on the mass, would these factors just be ignored by the fact that the bofy is moving with a constant velocity, thus, a=0, and the net force on the object is zero as well?
please help
thanks