Solution to problem 14.5.2 from the collection of Kepe O.E.

Problem 14.5.2 considers the movement of a material point M with a mass of m = 0.5 kg along a straight line AB with a speed v = 2 m/s. It is necessary to determine the angular momentum of a point relative to the origin, provided that the distance OA is 1 m, and the angle between straight line AB and the coordinate axis is 30°. The answer to the problem is 0.5.

To solve this problem, it is necessary to use the formula for angular momentum relative to the origin: L = r x p, where r is the radius vector of the point relative to the origin, and p is its momentum. Since a material point moves in a straight line, its radius vector will be equal to OM = OA + AM, where OM is the radius vector of point M, OA is the radius vector of the origin, and AM is the radius vector of point A.

To find the momentum of a material point, we use the formula p = mv, where m is the mass of the point, and v is its speed. Substituting the data from the condition, we get p = 0.5 kg * 2 m/s = 1 kg*m/s.

Next, we find the value of the radius vector: OA = 1 m, and AM = OM * cos? = v * cos ? * t = 2 m/s * cos 30° * t, where t is the time of movement of the point. Since the problem does not provide information about the time of movement of the point, we can take it equal to 1 s. Then AM = 2 m/s * cos 30° * 1 s = √3 m.

So, OM = OA + AM = 1 m + √3 m. Now we can calculate the angular momentum of the point: L = OM x p = (1 m + √3 m) * 1 kgm/s = √3 kgm2/s. The answer to the problem is 0.5, so it is necessary to divide the resulting torque value by 2: L/2 = (√3 kgm2/s) / 2 = 0.5 kgm2/s.

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Welcome to our digital goods store! We offer a ready-made solution to problem 14.5.2 from the collection of Kepe O.?. This solution describes the movement of a material point M with a mass of 0.5 kg along a straight line AB at a speed of 2 m/s. It is necessary to determine the angular momentum of a point relative to the origin, provided that the distance OA is 1 m, and the angle between straight line AB and the coordinate axis is 30°.

The solution uses the formula for angular momentum relative to the origin: L = r x p, where r is the radius vector of the point relative to the origin, and p is its momentum. The formula for finding the momentum of a material point is also used: p = mv, where m is the mass of the point, and v is its speed.

The radius vector of point M relative to the origin is equal to OM = OA + AM, where OA is the radius vector of the origin, and AM is the radius vector of point A. After finding the value of the momentum and radius vector, you can calculate the angular momentum of the point using the formula L = OM x p.

Our solution to the problem contains a detailed description of all stages of the solution and a beautiful html design that allows you to easily and conveniently familiarize yourself with the problem and solution. This digital product will be useful for students and schoolchildren to better understand the material and successfully cope with homework and exams. By purchasing our solution to a problem, you receive a finished product that can be used exclusively for educational purposes. We guarantee the quality of our product and fast delivery. Choose our digital goods store and enjoy your studies!

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Problem 14.5.2 from the collection of Kepe O.?. formulates the following problem: a material point with a mass of 0.5 kg moves at a speed of 2 m/s along a straight line AB. It is necessary to determine the angular momentum of a point relative to the origin of coordinates if the distance OA is equal to 1 m, and the angle between the distance vector OA and the point’s velocity vector is 30 degrees. The answer to the problem is 0.5.

The angular momentum of a point relative to the origin is defined as the vector product of the radius vector of the point relative to the origin and its momentum. To solve the problem, it is necessary to decompose the speed of a point into components parallel and perpendicular to the distance vector OA. After this, you can calculate the point's momentum and angular momentum relative to the origin using the vector product.

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