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lilyE

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I've spent at least an hour trying to figure this out, but can't seem to figure out how to solve this.

A 170g , 30.0-cm-diameter turntable rotates on frictionless bearings at 66.0rpm . A 25.0g block sits at the center of the turntable. A compressed spring shoots the block radically outward along a frictionless groove in the surface of the turntable.

What is the turntable's rotation angular velocity when the block reaches the outer edge?

Conservation of momentum: Ii*wi = If*wf

I(turntable) = Mr^2 = (.170 kg)(.15 m)^2 = 3.825*10^-3 kg m^2

I(block)o = mr^2 = 0

I(block)f = mr^2 = (.025 kg)(.15 m)^2 = 5.265*10^-4 kg m^2

wi = ((66 rpm)(2pi))/60 = 6.91 rad/s

I(turntable+block)f = 3.825*10^-3 + 5.265*10^-4 = 4.3875*10^-3 kg m^2

(3.825*10^-3)(6.91) = (4.3875*10^-3)wf

0.1826 = (4.3875*10^-3)wf

wf = 6.02 rad/s -- wrong

Initially, I tried using conservation of energy, and ended up with 5.52 rad/s. The program told me "not quite" and suggested a rounding error, so I think 5.52 might be close to the right answer, but I can't seem to figure out why I'm not getting it. Any help would be much appreciated!

1. Homework Statement1. Homework Statement

A 170g , 30.0-cm-diameter turntable rotates on frictionless bearings at 66.0rpm . A 25.0g block sits at the center of the turntable. A compressed spring shoots the block radically outward along a frictionless groove in the surface of the turntable.

What is the turntable's rotation angular velocity when the block reaches the outer edge?

## Homework Equations

Conservation of momentum: Ii*wi = If*wf

## The Attempt at a Solution

I(turntable) = Mr^2 = (.170 kg)(.15 m)^2 = 3.825*10^-3 kg m^2

I(block)o = mr^2 = 0

I(block)f = mr^2 = (.025 kg)(.15 m)^2 = 5.265*10^-4 kg m^2

wi = ((66 rpm)(2pi))/60 = 6.91 rad/s

I(turntable+block)f = 3.825*10^-3 + 5.265*10^-4 = 4.3875*10^-3 kg m^2

(3.825*10^-3)(6.91) = (4.3875*10^-3)wf

0.1826 = (4.3875*10^-3)wf

wf = 6.02 rad/s -- wrong

Initially, I tried using conservation of energy, and ended up with 5.52 rad/s. The program told me "not quite" and suggested a rounding error, so I think 5.52 might be close to the right answer, but I can't seem to figure out why I'm not getting it. Any help would be much appreciated!

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