Solution to problem 11.5.4 from the collection of Kepe O.E.

11.5.4 Point M moves with a constant speed v = 2 m/s but a ring of radius r = 0.5 m, which rotates with a constant angular speed ω = 4 rad/s. Determine the absolute acceleration module of point M in the indicated position. (Answer 16)

In this problem there is a point M moving at a constant speed v = 2 m/s along a ring of radius r = 0.5 m, which rotates at a constant angular speed ω = 4 rad/s. It is necessary to find the absolute acceleration modulus of point M in a given position. The solution to the problem is the number 16.

Solution to problem 11.5.4 from the collection of Kepe O.?.

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Digital product "Solution to problem 11.5.4 from the collection of Kepe O.?." is an electronic document in a beautiful html format that will help you successfully solve the problem in physics. In the problem there is a point M moving at a constant speed v = 2 m/s along a ring of radius r = 0.5 m, which rotates at a constant angular speed ω = 4 rad/s. The solution to the problem is the modulus of the absolute acceleration of point M in a given position, which is equal to 16. The document contains a detailed solution to the problem, as well as explanations and recommendations for a better understanding of the material and preparation for exams. Purchasing this digital product is a convenient and fast way to get the information you need and solve a complex physics problem in the shortest possible time.

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To problem 11.5.4 from the collection of Kepe O.?.:

Hopefully:

• speed of point M, v = 2 m/s
• ring radius, r = 0.5 m
• angular velocity of ring rotation, ω = 4 rad/s

Find:

• absolute acceleration module of point M in the indicated position

Solution: To find the absolute acceleration of point M, we use the formula for calculating acceleration when moving along a curve:

a = v^2 / r + rω^2

Where:

• v - speed of point M
• r - ring radius
• ω - angular velocity of ring rotation

Substituting the known values, we get:

a = 2^2 / 0.5 + 0.5 * 4^2 = 4 + 8 = 12 (m/s^2)

Answer: the absolute acceleration module of point M in the indicated position is 12 m/s^2.

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