Solution to problem 9.2.8 from the collection of Kepe O.E.

In blocks 1 and 2, the angular velocities of rotation around the fixed axes O1 and O2 are specified, respectively: ?1 = 4 rad/s and ?2 = 8 rad/s. The radii of the blocks are equal and amount to r = 10 cm. It is required to determine the angular velocity of the moving block 3. It rotates around the O3 axis, which is at an angle of 45° to the O1 axis.

To solve the problem it is necessary to use the laws of conservation of angular momentum. From these laws it follows that the sum of the angular momenta of all blocks relative to any axis remains unchanged in time. Thus, the following equation can be written:

I1 ?1 + I2 ?2 = I3 ?3,

where I1, I2 and I3 are the moments of inertia of blocks 1, 2 and 3, respectively, and ?3 is the desired angular velocity of the moving block.

The radii of the blocks are the same, therefore, their moments of inertia are also equal: I1 = I2 = I, where I = mr²/2 is the moment of inertia of one block relative to its axis of rotation.

Substituting these values ​​into the equation, we get:

2I ?3 = I ?1 + I ?2,

?3 = (I ?1 + I ?2) / (2I) = (?1 + ?2) / 2 = (4 rad/s + 8 rad/s) / 2 = 6 rad/s.

Thus, the angular velocity of the moving block is 6 rad/s.

Solution to problem 9.2.8 from the collection of Kepe O.?.

?electronic product "Solution to problem 9.2.8 from the collection of Kepe O.?" is an educational material containing a detailed solution to the specified problem in physics.

This product is intended for students and teachers who study physics and want to gain a deeper understanding of solving problems on this topic.

The solution to the problem is presented in the form of a text description, with a step-by-step solution algorithm and detailed calculations. In addition, the solution uses the laws of conservation of angular momentum, which makes it possible to more fully and accurately characterize the process of rotation of blocks in the problem.

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?electronic product "Solution to problem 9.2.8 from the collection of Kepe O.?" is a detailed solution to a physics problem. The problem considers the rotation of three blocks around their axes. Blocks 1 and 2 rotate around fixed axes O1 and O2, respectively, with given angular velocities ?1 = 4 rad/s and ?2 = 8 rad/s. It is required to determine the angular velocity of the moving block 3, which rotates around the O3 axis, located at an angle of 45° to the O1 axis. To solve the problem, the law of conservation of angular momentum is used, according to which the sum of the angular momentum of all blocks relative to any axis remains constant in time.

To solve the problem, a formula is used for the moment of inertia of one block relative to its axis of rotation, which is equal to I = mr²/2. The equality of the moments of inertia of blocks 1 and 2 (I1 = I2 = I) is also used, since their radii are the same. Substituting the values ​​into the equation, we obtain the angular velocity of moving block 3: ?3 = (I?1 + I?2) / (2I) = (?1 + ?2) / 2 = (4 rad/s + 8 rad/s) / 2 = 6 rad/s.

This electronic product is intended for students and teachers who are studying physics and want to gain a deeper understanding of solving problems on this topic. The solution to the problem is presented in the form of a text description, with a step-by-step solution algorithm and detailed calculations. The product format is pdf, which makes it a convenient and accessible tool for studying and preparing for exams.

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This product is a solution to problem 9.2.8 from the collection of Kepe O.?. The task is to determine the angular velocity of moving block 3 if blocks 1 and 2 rotate around the fixed axes O1 and O2 with angular velocities ?1 = 4 rad/s and ?2 = 8 rad/s. The radii of all blocks are the same and equal to r = 10 cm.

The answer to the problem is 2.

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