Rotational Motion and Moment of Inertia Questions

[hoseA]

1.)

A uniform rod of mass 0.93 kg is 17 m long.
The rod is pivoted about a horizontal, fric-
tionless pin at the end of a thin extension (of
negligible mass) a distance 17 m from the cen-
ter of mass of the rod. Initially the rod makes
an angle of 70 degrees with the horizontal. The rod
is released from rest at an angle of 70 degrees with
the horizontal.
The acceleration of gravity is 9.8 m/s^2.
Hint: The moment of inertia of the rod
about its center-of-mass is 1/12 ML^2.

What is the angular speed of the rod at
the instant the rod is in a horizontal position?
Answer in units of rad/s.

MgL/2 = .5(1/12ML^2)w^2

This works out to be:

w = sqrt(12g/L)

w = 2.630142 ?

But the answer is wrong?? why?!
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2.
Two pulley wheels, or respective radii R1 =
0.34 m and R2 = 1.5 m are mounted rigidly
on a common axle and clamped together. The
combined moment of inertia of the two wheels
is I + 4.5 kg*m^2.
Mass m1 = 18 kg is attached to a cord
wrapped around the first wheel, and another
mass m2 = 5.9 kg is attached to another cord
wrapped around the second wheel.

The acceleration of gravity is 9.8 m/s^2 :
Find the angular acceleration of the system.
Take clockwise direction as positive. Answer
in units of rad/s^2.

I = .5MR^2

I1= .5(18)(.34)^2
I2= .5(5.9)(1.5)^2

I = I1 +I2 + 4.5 = 12.1779

Acceleration= [(m2gR2)-(m1gR1)]/[I+(m1r1^2)+(m2r2^2)]

= .971689752 ??

This is wrong as well, WHY??!?

Please help. All help is appreciated.

 

[hoseA]

someone pls help me!... any hints appreciated. :)

 

[siddharth]

What is the angular speed of the rod at
the instant the rod is in a horizontal position?
Answer in units of rad/s.
MgL/2 = .5(1/12ML^2)w^2

How did you get that equation? Where have you used the fact that the rod is initially inclined at an angle of 70 degrees to the horizontal?

 

[hoseA]

How did you get that equation? Where have you used the fact that the rod is initially inclined at an angle of 70 degrees to the horizontal?

What equation should I use then?

I found a similar pbm online that used that equation- apparently it's wrong.

 

[siddharth]

Well, have you thought about what concept or principle you might use to attempt this question?

 

[hoseA]

Well, have you thought about what concept or principle you might use to attempt this question?

I know it uses Moment of Inertia in the equation... that's abt it.

I'm totally lost as to how to approach it.

 

[siddharth]

I'm totally lost as to how to approach it.

I understand that, but it's important to think in terms of principles and concepts rather than equations. The equations will easily follow once you understand what's happening.
For instance,in this problem, what can you say about the energy of the system?

 

[hoseA]

I understand that, but it's important to think in terms of principles and concepts rather than equations. The equations will easily follow once you understand what's happening.
For instance,in this problem, what can you say about the energy of the system?

Well, my brain isn't working at the moment.

I'll look at this tomorrow. Thanks for your help, nandrie, vannakam _/\_ ;).