Solution to problem 15.6.3 from the collection of Kepe O.E.

In this problem, the body has a vertical fixed axis of rotation and an initial angular velocity ?0 = 2.24 rad/s. The moment of inertia of the body relative to the axis of rotation is I = 8 kg•m2. The body is subject to a constant friction moment of the bearings M = 1 N•m. It is necessary to determine at what angle the body will turn before stopping.

To solve the problem, we use the equation of rotational motion:

ΔL = MΔt,

where ΔL is the change in the angular momentum of the body, M is the moment of forces acting on the body, Δt is the time of action of the moment.

Since the friction moment is constant, we can write:

ΔL = MΔt = -Мt,

where the “-” sign indicates that the friction moment is directed opposite to the angular velocity of rotation of the body.

To determine the angle of rotation of the body, we use the definition of angular momentum:

L = Iω,

where L is the angular momentum of the body, ω is the angular velocity of rotation of the body, I is the moment of inertia of the body relative to the axis of rotation.

Using these equations one can obtain:

ΔL = L - L0 = Iω - Iω0 = -Мt,

where L0 is the initial angular momentum of the body.

From here we can express the angle of rotation of the body before stopping:

θ = ΔL/I = -Мt/I = -M/I * t.

Substituting the known values, we get:

θ = (-1 N•m / 8 kg•m2) * (2.24 rad/s) / (1 N•m) * (1 s) = -0.28 rad.

The angle of rotation of the body before stopping will be 0.28 radians, which corresponds to approximately 20.1 degrees.

Solution to problem 15.6.3 from the collection of Kepe O.?.

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This product is a solution to problem 15.6.3 from the collection of problems in physics by Kepe O.?.

The problem considers a rigid body with a vertical fixed axis of rotation. The initial angular velocity of the body is known ?0 = 2.24 rad/s, the moment of inertia of the body relative to the axis of rotation I = 8 kg • m2 and the constant friction moment of the bearings M = 1 N • m acting on the body.

It is necessary to determine at what angle the body will turn before stopping.

The solution to this problem is to determine the angular acceleration of the body using the equation of rotational motion. Then you need to determine the time during which the body will stop. And finally, using the formula for the angle of rotation of a rotating body, you can find the answer to the problem.

The result of solving the problem is the answer: 20.1 degrees.

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