Where do I go wrong?

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Homework Statement



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The Attempt at a Solution



A) for disk,[/B]

let w is the angular speed of the disk at the lowest point.

moment of Inertia of disk about pivot, P = 0.5*M*R^2 + M*R^2

= 1.5*M*R^2

Apply conservation of energy

initial potentila energy = finalkinetic energy


m*g*R = (1/2)*I*w^2

m*g*R = (1/2)*1.5*m*R^2*w^2

m*g*R = (1/2)*1.5*m*(R^2*w^2)

g*R = (1/2)*1.5*v_disk^2

2*g*R = 1.5*v_disk^2

v_disk = sqrt(2*g*R)/sqrt(1.5)

= 0.816*sqrt(2*g*R)

= 0.816*v <<<<<<------Answer (wrong! and i don't know why)


B) for hoop,

let w is the angular speed of the hoop at the lowest point.

moment of Inertia of hoop about pivot, P = M*R^2 + M*R^2

= 2*M*R^2

Apply conservation of energy

initial potentila energy = finalkinetic energy


m*g*R = (1/2)*I*w^2

m*g*R = (1/2)*2*m*R^2*w^2

m*g*R = (1/2)*2*m*(R^2*w^2)

g*R = (1/2)*2*v_hoop^2

2*g*R = 2*v_hoop^2

v_hoop = sqrt(2*g*R)/sqrt(2)

= 0.707*sqrt(2*g*R)

= 0.707*v <<<<<<------Answer ( wrong and i don't know why)
 

Answers and Replies

  • #2
andrewkirk
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In both the disk and the hoop problem, when you convert angular velocity to linear velocity of the lowest point, you use R as the radius. What is the distance from the lowest point to the axis of rotation?
 
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In both the disk and the hoop problem, when you convert angular velocity to linear velocity of the lowest point, you use R as the radius. What is the distance from the lowest point to the axis of rotation?
Thanks!!I got it!!
 

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