# Period of oscillation of a rocking semi cylinder?

• jaron_denson
In summary, the problem involves a thin rectangular plate being bent into a semicircular cylinder and determining the period of oscillation when it is allowed to rock on a horizontal surface. The solution requires knowing the moment of inertia of a half cylinder, which can be calculated using the mass, width, and length of the plate.
jaron_denson

## Homework Statement

a thin rectangular plate is bent into a semicircular cylinder, dertermine the period of oscillation if it is allowed to rock on a horizantal surface.

## The Attempt at a Solution

So I can figure out the rest of the problem if I know what the moment of inertia of a half cylinder is. My side note is a guess, but not sure if it is correct. I checked around online couldn't find anything that helpful

.Assuming the plate is uniform with mass m and width w and length l then the moment of inertia can be calculated as I = 1/2ml^2 + 1/3mw^2

.The period of oscillation of a rocking semi cylinder can be determined using the principles of simple harmonic motion. The moment of inertia of a half cylinder can be calculated using the formula I = (1/2)MR^2, where M is the mass of the cylinder and R is the radius of the cylinder. Once the moment of inertia is known, the period of oscillation can be calculated using the formula T = 2π√(I/mgd), where m is the mass of the cylinder, g is the acceleration due to gravity, and d is the distance from the center of mass to the pivot point. This formula assumes that the rocking motion is small and the cylinder behaves like a simple pendulum. Alternatively, if the rocking motion is large, the period of oscillation can be calculated using the formula T = 2π√(I/mgR), where R is the radius of the cylinder. I hope this helps.

## 1. What is the period of oscillation for a rocking semi cylinder?

The period of oscillation for a rocking semi cylinder is the amount of time it takes for the cylinder to complete one full back-and-forth motion.

## 2. How is the period of oscillation calculated for a rocking semi cylinder?

The period of oscillation for a rocking semi cylinder can be calculated using the formula T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance between the center of mass and the pivot point.

## 3. What factors affect the period of oscillation for a rocking semi cylinder?

The period of oscillation for a rocking semi cylinder is affected by factors such as the mass of the cylinder, the distance between the center of mass and the pivot point, and the acceleration due to gravity.

## 4. How does the angle of the semi cylinder's initial position affect its period of oscillation?

The angle of the semi cylinder's initial position does not affect its period of oscillation. As long as the cylinder is able to rock back and forth, the period will remain the same regardless of the initial angle.

## 5. Can the period of oscillation for a rocking semi cylinder be changed?

Yes, the period of oscillation for a rocking semi cylinder can be changed by altering the factors that affect it, such as the mass, distance, and acceleration due to gravity. For example, increasing the mass of the cylinder will result in a longer period, while increasing the distance or acceleration due to gravity will result in a shorter period.

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