Solve Rotational Questions for Translational Speeds & Angular Speed

[clphipps]

Homework Statement

Consider two objects with m1>m2 connected by a light string that passes over a pulley having a moment of inertia of I about the axis of rotation. The string does not slip on the pulley or stretch. The pulley turns without friction. The two object are released from rest by a vertical distance of 9h.

Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other?

Find the angular speed of the pulley at this time?

Homework Equations

The Attempt at a Solution

 

[member 553083]

Conservation of energy: 1/2m1v1^2 + 1/2m2v2^2 + 1/2Iω^2 = mgh Using this equation and substituting the values given, we have 1/2m1v1^2 + 1/2m2v2^2 + 1/2Iω^2 = 9mg We can solve for v1 and v2 by rearranging the equationv1^2 = 2(9mg - 1/2m2v2^2 - 1/2Iω^2)/m1 v2^2 = 2(9mg - 1/2m1v1^2 - 1/2Iω^2)/m2 We can then solve for ω using either equationω^2 = 2(9mg - 1/2m1v1^2 - 1/2m2v2^2)/I Therefore, the translational speeds of the objects as they pass each other is v1 and v2, and the angular speed of the pulley is ω.