Solution to problem 8.3.16 from the collection of Kepe O.E.

8.3.16 The acceleration of point M of a disk rotating around a fixed axis is 8 m/s2.

Determine the angular acceleration of this disk if its radius R = 0.4 m and angle α = 30°. (Answer 10)

To solve this problem, you need to use the formula for the acceleration of a point on a circle:

a = R * a'

where a is the acceleration of a point on a circle, R is the radius of the circle, α' is the angular acceleration.

Substituting known values, we get:

8 m/s² = 0.4 m * α'

α' = 20 rad/s²

Next, using the formula for the relationship between linear velocity and angular velocity:

v = R * ω

where v is the linear speed of a point on a circle, ω is the angular speed, R is the radius of the circle.

Substituting known values, we get:

v = 0.4 m * ω

Since the point is located at a distance of 30° from the initial position, the angular distance traveled by the point during the acceleration time is equal to 30°.

Using the formula for the relationship between angular distance and angular velocity:

φ = ω * t

where φ is the angular distance traveled by the point in time t, ω is the angular velocity.

Substituting known values, we get:

30° = ω * t

t = 30° / ω

Thus, the angular acceleration of the disk is 20 rad/s², and the time it takes the point to travel an angular distance of 30° is 1.5 seconds.

Solution to problem 8.3.16 from the collection of Kepe O.?.

We present to your attention the solution to one of the problems from the collection of Kepe O.?. - "Physics workbook for university students."

In this problem, we consider the acceleration of a point on a circle and find the angular acceleration of a disk rotating around a fixed axis. Our solution contains a detailed description of all the necessary formulas and solution steps.

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Price: 100 rubles.

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This product is a solution to problem 8.3.16 from the collection of Kepe O.?. in physics. The problem is to determine the angular acceleration of a disk rotating around a fixed axis with a known acceleration of a point on its circumference, radius and angle. To solve the problem it is necessary to use the appropriate formulas and principles of physics. Solving a problem involves stating the problem, using the necessary formulas, substituting known values, doing calculations, and obtaining the answer. The answer to the problem is 10.

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