Moment of Inertia & Mass Distribution Video Lessons

Video Thumbnail

Concept

Problem: A thin rod of mass mr and length 2L is allowed to pivot freely about its center, as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward, with the magnitude of the gravitational acceleration equal to g.Part AWhat is the moment of inertia I of this assembly about the axis through which it is pivoted?Express the moment of inertia in terms of mr, m1, m2, and L. Remember, the length of the rod is 2L, not L.Part BSuppose the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol I, the moment of inertia of the assembly, whether or not you have answered the first part correctly.)What is the angular acceleration α of the rod immediately after it is released?Take the counterclockwise direction to be positive. Express α in terms of some or all of the variables mr, m1, m2, L, I, and g.

FREE Expert Solution

Part A

Moment of inertia of a thin rod about its center is:

I=mL212

Therefore,

79% (171 ratings)
View Complete Written Solution
Problem Details

A thin rod of mass mr and length 2L is allowed to pivot freely about its center, as shown in the diagram. A small sphere of mass m1 is attached to the left end of the rod, and a small sphere of mass m2 is attached to the right end. The spheres are small enough that they can be considered point particles. The gravitational force acts downward, with the magnitude of the gravitational acceleration equal to g.

MRB_mi_6.jpg

Part A

What is the moment of inertia I of this assembly about the axis through which it is pivoted?

Express the moment of inertia in terms of mr, m1, m2, and L. Remember, the length of the rod is 2L, not L.


Part B

Suppose the rod is held at rest horizontally and then released. (Throughout the remainder of this problem, your answer may include the symbol I, the moment of inertia of the assembly, whether or not you have answered the first part correctly.)

What is the angular acceleration α of the rod immediately after it is released?

Take the counterclockwise direction to be positive. Express α in terms of some or all of the variables mr, m1, m2, L, I, and g.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Moment of Inertia & Mass Distribution concept. You can view video lessons to learn Moment of Inertia & Mass Distribution. Or if you need more Moment of Inertia & Mass Distribution practice, you can also practice Moment of Inertia & Mass Distribution practice problems.