Horizontal platform with a mass of 100 kg and a radius of 1 m

Horizontal platform with a mass of 100 kg and a radius of 1 m

This digital product is a detailed description of a horizontal platform weighing 100 kg and radius 1 m, made in a beautiful html format.

The description contains the exact scientific data and formulas necessary to understand the principles of the platform, which makes it useful for students, teachers and anyone interested in physics and mechanics.

The description is designed in a modern style, which makes it convenient and attractive for reading and studying.

This digital product is an indispensable resource for learning and understanding the scientific principles behind the operation of such devices. It may be of interest to both beginners and experienced specialists in the field of mechanics and physics.

This digital product is a detailed description of a horizontal platform with a mass of 100 kg and a radius of 1 m, which rotates with a frequency n1 = 0.5 rpm around a vertical axis passing through the center of inertia of the platform. A person weighing 60 kg stands on the edge of the platform. The task is to determine at what frequency n2 the platform will rotate if a person steps off it. The platform is considered a disk, and a person is considered a material point.

To solve the problem, it is necessary to use the law of conservation of angular momentum. Initially, when a person is on the platform, the angular momentum of the system is equal to the sum of the angular momentum of the platform and the person, i.e. the mass of the platform multiplied by its radius multiplied by its angular velocity, plus the mass of the person multiplied by the radius of the platform multiplied by its angular velocity.

L1 = I1 * n1 + m * R * n1,

where L1 is the moment of impulse of the system before the person leaves the platform, I1 is the moment of inertia of the platform relative to the vertical axis passing through the center of inertia of the platform, m is the mass of the person, R is the radius of the platform, n1 is the angular velocity of the platform.

When a person leaves the platform, the angular momentum of the system will change. Let's calculate it using the fact that at the final moment of time the angular momentum of the system must be conserved:

L2 = I2 * n2,

where L2 is the angular momentum of the system after the person leaves the platform, I2 is the moment of inertia of the platform after the person leaves the platform, n2 is the angular velocity of the platform after the person leaves the platform.

Since the angular momentum of the system must be conserved, L1 must be equal to L2:

I1 * n1 + m * R * n1 = I2 * n2.

The moment of inertia of the disk can be calculated using the formula:

I = (m * R^2) / 2,

where m is the mass of the disk, R is its radius.

Then the moment of inertia for the platform will be equal to:

I1 = (100 * 1^2) / 2 = 50 kg*m^2.

The moment of inertia of the platform after a person leaves it will be equal to the moment of inertia of a disk with a mass of 100 kg and a radius of 1 minus the moment of inertia of a material point with a mass of 60 kg and a radius of 1 m:

I2 = (100 * 1^2) / 2 - 60 * 1^2 = 40 kg*m^2.

Substitute the values ​​into the equation:

50 * 0.5 + 60 * 1 * 0.5 = 40 * n2.

From here we get:

n2 = (50 * 0.5 + 60 * 1 * 0.5) / 40 = 0.875 rps.

Thus, after a person leaves the platform, its angular speed will increase to 0.875 rps.

This product description contains not only a solution to a specific problem, but also a general description of a horizontal platform with a mass of 100 kg and a radius of 1 m. Including a description of its moment of inertia and angular velocity at the initial moment of time. The description also contains formulas and laws used in solving the problem, which allows you to more deeply understand the physical principles underlying this problem. The description is designed in a modern style, which makes it convenient and attractive for reading and studying. Thus, this digital product is a useful resource for learning and understanding the science behind such devices.

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The horizontal platform has a mass of 100 kg and a radius of 1 meter. The platform rotates with a frequency n1=0.5 revolutions per second around a vertical axis passing through the center of inertia of the platform. Additionally, on the platform there is a person weighing 60 kg, who stands on the edge of the platform. The platform can be considered a disk, and a person - a material point.

To solve the problem, it is necessary to use the laws of conservation of momentum and angular momentum. Before the person leaves the platform, the total angular momentum of the system (platform + person) is conserved. This means that the angular momentum of the system before and after the person’s separation from the platform will be equal.

From the law of conservation of angular momentum, one can find the angular velocity of the platform after the person leaves it. In this case, we can assume that the moment of inertia of the platform will not change after the person is separated.

So, let n2 be the desired rotation speed of the platform after the person gets off it. Let us denote the moment of inertia of the platform as I, and the angular velocity of the platform before and after the person is lifted off as omega1 and omega2, respectively.

The total angular momentum of the system before the person is separated: L1 = I * omega1 + m * R * omega1,

where m is the mass of the person, R is the radius of the platform.

The total angular momentum of the system after the person is separated: L2 = I * omega2.

From the law of conservation of angular momentum L1=L2 we obtain: I * omega1 + m * R * omega1 = I * omega2,

from where: omega2 = (I * omega1) / (I + m * R^2).

Substituting the values, we get: omega2 = (100 kg * 1 m^2 * (0.5 rps)) / (100 kg * 1 m^2 + 60 kg * 1 m^2) = 0.29 rps.

Answer: the platform will rotate with a frequency of n2=0.29 r/s when a person gets off it.

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1. The horizontal platform is perfect for conducting physical experiments and measurements.
2. This platform is made of durable materials and can withstand significant loads.
3. Thanks to its horizontal design, the platform ensures stability and accuracy of measurements.
4. The radius of the platform allows you to experiment with various objects of different sizes and shapes.
5. This platform is easy to assemble and disassemble, making it convenient for transportation and storage.
6. The platform has a wide range of applications in various fields, including science, engineering and industry.
7. The horizontal platform weighs 100 kg and has a radius of 1 m and is an excellent choice for anyone looking for a reliable and precise instrument for carrying out experiments and research.

Peculiarities:

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