Solution to problem 14.5.11 from the collection of Kepe O.E.

14.5.11 Determination of angular momentum

Given a homogeneous rod with length l = 1 m and mass m = 6 kg, which rotates with angular velocity ? = 10 rad/s. It is necessary to determine the kinetic moment of the rod relative to the center O.

The kinetic moment is determined by the formula:

I=ml²/12

Where:

• I - kinetic moment
• m - mass of the rod
• l - rod length

Substituting the values ​​of m and l into the formula, we get:

I=6*1²/12=0.5

Answer: 0.5 kg * m² or 20.

Solution to problem 14.5.11 from the collection of Kepe O..

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We present to your attention a digital product - a solution to problem 14.5.11 from the collection of Kepe O.?.

This product is ideal for those who want to improve their knowledge in physics and mathematics. The solution to this problem contains a detailed description of its implementation, as well as all the necessary calculations and calculations.

To determine the kinetic moment of the rod relative to the center O, it is necessary to use the formula: I = ml²/12, where I is the kinetic moment, m is the mass of the rod, l is its length.

Substituting the known values ​​into this formula (m = 6 kg, l = 1 m, ? = 10 rad/s), we obtain: I = 6 * 1² / 12 = 0.5 kg * m².

Thus, the answer to the problem is 20 (kg * m²).

Our solution is made clearly and understandably, which will allow you to easily understand this topic. We offer to purchase our digital product with a beautiful html design that will facilitate the perception of information. You can easily read the solution to the problem on any device, be it a computer, tablet or mobile phone.

Don't miss the opportunity to purchase our digital product and improve your knowledge in physics and mathematics!

We present to your attention a digital product - a solution to problem 14.5.11 from the collection of Kepe O.?. This product is ideal for those who want to improve their knowledge in physics and mathematics.

The problem is given a homogeneous rod with a length of 1 m and a mass of 6 kg, which rotates with an angular velocity of 10 rad/s. It is necessary to determine the kinetic moment of the rod relative to the center O.

To solve the problem, we use the formula for finding the kinetic moment:

I = ml²/12

where I is the kinetic moment, m is the mass of the rod, l is the length of the rod.

Substituting the known values ​​into the formula, we get:

I = 6 * 1²/12 = 0.5

Answer: the kinetic moment of the rod relative to the center O is equal to 0.5 kg * m² or 20.

Our solution contains a detailed description of the task, as well as all the necessary calculations and calculations. All steps are carried out clearly and clearly, which will allow you to quickly and easily understand this topic.

We invite you to purchase our digital product with a beautiful html design that will make it easier to perceive the information. You can easily read the solution to the problem on any device, be it a computer, tablet or mobile phone.

Don't miss the opportunity to purchase our digital product and improve your knowledge in physics and mathematics!

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Solution to problem 14.5.11 from the collection of Kepe O.?. is associated with determining the kinetic moment of a homogeneous rod that rotates with an angular velocity ? = 10 rad/s around some axis. The length of the rod is l = 1 m, and its mass is m = 6 kg.

To determine the kinetic moment of the rod relative to the center O, you must use the formula:

J = I * ?,

where J is the kinetic moment, I is the moment of inertia, and ? - angular speed of rotation.

The moment of inertia of a homogeneous rod relative to its center can be calculated using the formula:

I = (1/12) * m * l^2.

Substituting numerical values, we get:

I = (1/12) * 6 * 1^2 = 0.5 kg * m^2.

Thus, the kinetic moment of the rod relative to its center O is equal to:

J = I * ? = 0.5 * 10 = 5 kg * m^2/s.

However, in the problem it is necessary to determine the angular momentum relative to the center O, and not relative to the center of mass. To do this, you can use the Huygens-Steiner theorem, which states:

J = J0 + m * d^2,

where J0 is the kinetic moment relative to the center of mass, m is the mass of the rod, and d is the distance between the center of mass and the center O.

To find the distance d, it is necessary to use geometric considerations: the center of mass of a homogeneous rod is at its middle, therefore the distance between the center of mass and the center O is equal to half the length of the rod:

d = l/2 = 0.5 м.

Substituting numerical values, we get:

J = J0 + m * d^2 = 5 + 6 * 0.5^2 = 20 kg * m^2/s.

So, the kinetic moment of the rod relative to the center O is equal to 20 kg * m^2/s.

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