Rotational Inertia of Square Homework

In summary, the rotational inertia of this rigid body about an axis that (a) passes through the midpoints of opposite sides and lies in the plane of the square is 0.492 kgm^2, (b) passes through the midpoint of one of the sides and is perpendicular to the plane of the square is 0.493 kgm^2, and (c) lies in the plane of the square and passes through two diagonally opposite particles is 0.492 kgm^2.
  • #1
mmiller9913
14
0

Homework Statement



Four identical particles of mass 0.351 kg each are placed at the vertices of a 3.50 m x 3.50 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a) passes through the midpoints of opposite sides and lies in the plane of the square, (b) passes through the midpoint of one of the sides and is perpendicular to the plane of the square, and (c) lies in the plane of the square and passes through two diagonally opposite particles?

Homework Equations


I = mr^2
I = Icom + Mh^2

The Attempt at a Solution


a) I think you would do I = mr^2 + mr^2
so, I = 2(.351)(3.5/2)^2 + 2(.351)(3.5/2)^2

b) I = .351(3.5/2)^2 + .351(3.5/2)^2 + 2(.351)(3.5)^2

c) Since the diagonal of the square is 4.95m
I = .351(4.95/2)^2 +.351(4.95/2)^2

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
hi mmiller9913! :smile:

(try using the X2 icon just above the Reply box :wink:)
mmiller9913 said:
b) I = .351(3.5/2)^2 + .351(3.5/2)^2 + 2(.351)(3.5)^2

(a) and (c) are fine :smile:

try (b) again​
 

FAQ: Rotational Inertia of Square Homework

What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation.

How is rotational inertia calculated for a square?

The rotational inertia of a square can be calculated using the formula I = 1/6 * m * (a^2 + b^2), where m is the mass of the square, and a and b are the lengths of its sides.

How does the shape of a square affect its rotational inertia?

The rotational inertia of a square is affected by its shape in terms of its mass distribution. A square with a larger mass concentrated towards its edges will have a higher rotational inertia compared to a square with a more uniform mass distribution.

How does rotational inertia impact the rotation of a square?

The higher the rotational inertia of a square, the more difficult it is to change its rotation. This means that objects with higher rotational inertia will require more torque to rotate and will have a slower angular acceleration.

What are some real-life applications of understanding rotational inertia of squares?

Understanding rotational inertia is important in fields such as engineering, physics, and robotics. It is used in designing objects that need to rotate, such as wheels, gears, and flywheels. It is also crucial in understanding the motion of objects in space, such as planets and satellites.

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