Moment of Inertia + Energy question

In summary, the conversation discusses a uniform rod of mass 3 kg that is 17 m long and pivoted about a horizontal, frictionless pin. The rod is initially at an angle of 66◦ with the horizontal and is released from rest at the same angle. The question is asking for the angular speed of the rod when it is in a horizontal position. The suggested moment of inertia for the rod is 1/12mL^2. There is uncertainty about the value of h in the equation for angular speed.
  • #1
darkspym7
10
0

Homework Statement


A uniform rod of mass 3 kg is 17 m long. The rod is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligible mass) a distance 17 m from the center of mass of the rod. Initially the rod makes an angle of 66◦ with the horizontal. The rod is released from rest at an angle of 66◦ with the horizontal, as shown in the figure below The acceleration of gravity is 9.8 m/s2.
Hint: The moment of inertia of the rod about its center-of-mass is Icm = 1/12mL^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.


Homework Equations


U=mgh
K=1/2Iw^2


The Attempt at a Solution


The moment of inertia I got for the whole system was:
I=M(L/2)^2+1/12ML^2
I've managed to get:
w=[tex]\sqrt{\frac{6gh}{L^2}}}[/tex], with w being the angular speed
But I am unsure if h is L*sin(theta) or (3/2L)*sin(theta), since the rod is off the pivot.

Any ideas?
 
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  • #2
Here's the figure that went along with it:

http://img103.imageshack.us/img103/9987/hw10q1ex1.jpg
 
Last edited by a moderator:
  • #3
Anyone?
 
  • #4
I still don't know.
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to rotational motion, based on its mass and distribution of mass around an axis.

2. How is moment of inertia calculated?

The moment of inertia of a point mass is calculated by multiplying the mass by the square of the distance from the axis of rotation. For a continuous object, it is calculated by integrating the mass distribution over the object's volume.

3. What is the significance of moment of inertia?

Moment of inertia is important in the study of rotational motion, as it affects an object's angular acceleration and the amount of torque required to produce a certain amount of angular acceleration.

4. What is the relationship between moment of inertia and energy?

Moment of inertia and energy are related through the rotational kinetic energy equation, where the moment of inertia is in the denominator. This means that an object with a larger moment of inertia will have a lower rotational kinetic energy for the same angular velocity.

5. How does moment of inertia affect an object's stability?

Objects with a larger moment of inertia are more stable, as they require more torque to cause angular acceleration. This is why objects like spinning tops and gyroscope maintain their balance despite external forces.

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