Solution to problem 16.1.7 from the collection of Kepe O.E.

Is there a rotation equation? = 2sin(?t/2), describing a homogeneous rectangular plate with a moment of inertia about the axis of rotation Iz = 10 kg • m2. It is necessary to determine the main moment of external forces acting on the body at time t = 1 s. The answer to the problem is -49.3.

Solution to problem 16.1.7 from the collection of Kepe O.?.

This digital product is a solution to problem 16.1.7 from the collection of problems by Kepe O.?. in physics. The solution was completed by a professional teacher and guarantees full compliance with the conditions of the problem and the correctness of the answer.

The problem describes a homogeneous rectangular plate with a moment of inertia about the axis of rotation Iz = 10 kg • m2, which rotates according to the equation? = 2sin(?t/2). The solution allows us to determine the main moment of external forces acting on the body at time t = 1 s.

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Price: 100 rubles

This digital product is a solution to problem 16.1.7 from the collection of problems by Kepe O.?. in physics. The problem describes a homogeneous rectangular plate with a moment of inertia about the axis of rotation Iz = 10 kg • m2, which rotates according to the equation? = 2sin(?t/2). You need to determine the main moment of external forces acting on the body at time t = 1 s.

The solution was completed by a professional teacher and guarantees full compliance with the conditions of the problem and the correctness of the answer. By purchasing this digital product for 100 rubles, you receive a ready-made solution to the problem in PDF format, which can be used to prepare for exams, do homework and independently study physics.

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Solution to problem 16.1.7 from the collection of Kepe O.?. consists in determining the main moment of external forces acting on a homogeneous rectangular plate with a moment of inertia Iz = 10 kg • m2, at time t = 1 s. To solve the problem it is necessary to use the given rotation equation? = 2sin(?t/2).

First you need to determine the angular acceleration of the plate using the relationship between angular acceleration and angular displacement:

α = dω/dt = d²θ/dt²,

where ω is the angular velocity, θ is the angle of rotation of the plate.

Based on the given rotation equation, the angular velocity of the plate can be determined:

ω = dθ/dt = d(?t)/dt = ?/2 * cos(?t/2).

Then you need to find the angular acceleration:

α = dω/dt = d( ?/2 * cos(?t/2) )/dt = -?²/4 * sin(?t/2).

Next, using Newton’s second law for rotational motion, we can determine the main moment of external forces:

M = Iα,

where I is the moment of inertia of the plate relative to the axis of rotation.

Substituting the known values, we get:

M = Iz * α = 10 * (-?2/4 * sin(?t/2)) = -5?2 * sin(?/2) Н * м.

And finally, substituting t = 1 s and the value ? = 2sin(?t/2) we get:

M = -5(2sin(?/2))² * sin(?/2) = -5/4 * (2sin(?/2))^3 = -49,3 Н * м.

Thus, the main moment of external forces acting on the slab at time t = 1 s is equal to -49.3 N * m.

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