A massless rod of length L has a small mass m fastened at its center and another

ID: 3897381 • Letter: A

Question

A massless rod of length L has a small mass

m fastened at its center and another mass m

fastened at one end. On the opposite end

from the mass m, the rod is hinged with a

frictionless hinge. The rod is released from

rest from an initial horizontal position; then

it swings down.

What is the angular velocity as the rod

swings through its lowest (vertical) position?

1. sqrt(2g/L)

2.sqrt(2g/3L)

3. sqrt(4g/5L)

4. sqrt(5g/6L) 2nd choice, not correct either.

5. sqrt(3g/2L)

6. sqrt(6g/5L) 1st choice, not correct.

7. sqrt(12g/5L)

8. sqrt(g/4L)

9. sqrt(g/L)

10. sqrt(g/2L)

Conservation of energy

U top = K bottom

(m + m)*g*L = 1/2*I*?^2 where I = m*(L/2)^2 + m*L^2 = 1.25*m*L^2

So 2m*g*L = 1/2*1.25*m*L^2*?^2

So ? = sqrt(3*g*/(1.25*L) ) = sqrt(12g/5L)

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