Solution to problem 11.4.5 from the collection of Kepe O.E.

11.4.5. Given a semicircle that rotates around its diameter with an angular velocity ω = 4 rad/s. On the rim of this semicircle there is a point M, which moves with speed vr relative to the semicircle. It is necessary to find the Cornolis acceleration modulus of point M in a given position. Answer: 0.

So, we have a rotating semicircle with point M on its rim. Point M moves relative to the semicircle with speed vr. To find the Cornolis acceleration in a given position, we need to know the radius of curvature of the trajectory of point M and its angular velocity.

The radius of curvature of the trajectory of point M in this case is equal to the radius of the semicircle, since point M moves along its rim. The radius of a semicircle can be found by knowing its diameter. The diameter of a semicircle is equal to the length of the arc it describes in half a rotation period (since a semicircle describes a full rotation in two periods). The arc length of a semicircle is equal to πR, where R is the radius of the semicircle. Thus, the diameter of the semicircle is 2πR/2 = πR.

The angular velocity of rotation of the semicircle is already given and is equal to ω = 4 rad/s. The Cornolis acceleration of point M in this position is zero, since the speed of point M relative to the semicircle does not change.

Our digital goods store presents you with a unique product - a solution to problem 11.4.5 from the collection of Kepe O.?. This digital product is intended for everyone who is faced with problems in physics and mathematics and is looking for a quality solution.

The product is designed in a beautiful html format, which makes it convenient and easy to use. You can easily read the solution to the problem, see all the stages of the solution and get a detailed explanation of each step.

Solution to problem 11.4.5 from the collection of Kepe O.?. is an excellent choice for anyone who wants to improve their knowledge of physics and mathematics, as well as for pupils, students and teachers. Thanks to our digital product, you can easily understand the material, improve your skills and successfully cope with any task.

Our digital goods store presents you with the solution to problem 11.4.5 from the collection of Kepe O.?. This problem describes the movement of point M on the rim of a rotating semicircle with angular velocity ω = 4 rad/s relative to the semicircle with speed vr. To find the Cornolis acceleration modulus of point M in a given position, you need to know the radius of curvature of the trajectory of point M and its angular velocity. The radius of curvature of the trajectory is equal to the radius of the semicircle, since point M moves along its rim, which can be found by knowing the diameter of the semicircle. The diameter of a semicircle is equal to the length of the arc it describes in half the rotation period, that is, πR, where R is the radius of the semicircle. The angular velocity of rotation of the semicircle is already given and is equal to ω = 4 rad/s. The Cornolis acceleration of point M in this position is zero, since the speed of point M relative to the semicircle does not change. The solution to the problem is presented in a beautiful html format and contains a detailed explanation of each step. This digital product will help you better understand physics and improve your skills in solving similar problems.

***

The product is the solution to problem 11.4.5 from the collection of Kepe O.?.

The problem describes the movement of point M along the rim of a semicircle, which rotates around its diameter with an angular velocity ω = 4 rad/s. The value of the relative speed of point M, designated as vr, is given. It is necessary to determine the Cornolis acceleration modulus of point M in the specified position at which the answer is 0.

The Cornolis acceleration modulus is a value equal to the product of the square of the angular velocity and the radius of curvature of the point's trajectory. The trajectory of point M is a circle, which means the radius of curvature is equal to the radius of the semicircle.

To solve the problem, it is necessary to calculate the radius of curvature and substitute the value into the formula for the Cornolis acceleration modulus. Considering that the answer to the problem is 0, we can assume that the relative speed of point M is equal to the angular speed multiplied by the radius of curvature of the trajectory, since in this case point M moves in a circle at a constant speed. Then from the equation vr = ω * R it follows that R = vr / ω.

Substituting the known values ​​into the formula for the Cornolis acceleration modulus, we obtain:

a = ω^2 * R = ω^2 * (vr / ω)^2 = vr^2 / R

a = vr^2 * ω^2 / vr = vr * ω^2

The answer to the problem will be a = 0, which corresponds to the answer given in the condition.

***

1. Solution to problem 11.4.5 from the collection of Kepe O.E. is an excellent digital product for mathematics students and teachers.
2. Thanks to this solution, you can quickly and easily learn to solve complex mathematical problems.
3. Solution to problem 11.4.5 from the collection of Kepe O.E. is a convenient and effective way to improve your level of knowledge in mathematics.
4. I really liked that the solution to problem 11.4.5 from the collection of Kepe O.E. available in electronic form - this greatly simplifies the learning process.
5. With this solution, you can easily understand complex mathematics topics and apply the acquired knowledge in practice.
6. I used the solution to problem 11.4.5 from the collection of O.E. Kepe. to prepare for exams and was able to successfully cope with the tests.
7. I recommend this solution to anyone who wants to improve their math skills and achieve academic success.

Peculiarities:

A very handy digital product for solving math problems.

Thanks to this solution of the problem from the collection of Kepe O.E., my preparation for the exam has become more effective.

The solution of problem 11.4.5 has become an indispensable assistant in preparing for lessons and tests.

A quick and high-quality solution to problem 11.4.5 thanks to a digital product.

It is very easy to use this solution to the problem, even if you are not very strong in mathematics.

With this solution to the problem, I was able to better understand the mathematical material and improve my knowledge.

This solution to the problem helped me save a lot of time, which I could spend on more important tasks.