Solution to problem 17.3.18 from the collection of Kepe O.E.

17.3.18 On a round object of radius r = 0.2 m, which rotates with angular acceleration ϵ = 20 rad/s2, a pair of forces arises with a moment M = 1.5 N m, as well as a force T. The moment of inertia of the object relative to it axis of rotation is 0.05 kg m2. It is necessary to determine which module the force T has.

Solution: The moment of forces acting on an object is equal to the sum of the moments created by each of the forces: M = M1 + M2

where M1 is the moment of a pair of forces, M2 is the moment of force T.

Considering that the moment of inertia of the object is equal to I, and its angular acceleration is equal to ε, we obtain the formula:

М = I·e

Thus,

M1 + M2 = I·ε

M1 = I·ε - M2

Substituting the known values, we get:

1.5 N m + M2 = 0.05 kg m2 20 rad/s2

M2 = 2.5 N

Answer: force modulus T is 2.5 N.

Solution to problem 17.3.18 from the collection of Kepe O.?.

This digital product is the solution to problem 17.3.18 from the collection of Kepe O.?. This solution is intended for students and anyone studying physics and mathematics.

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Product description: this is the solution to problem 17.3.18 from the collection of Kepe O.?. in physics. The problem is to determine the magnitude of the force T acting on a wheel of radius r = 0.2 m, which rotates with angular acceleration ϵ = 20 rad/s2. The wheel is acted upon by a pair of forces with a moment M = 1.5 N m and a force T. The moment of inertia of the wheel relative to its axis of rotation is 0.05 kg m2.

The solution to the problem is based on formulas and proven methods, which are described in detail in the solution. After purchase, you will be able to download the solution file in PDF format and use it for your educational purposes. The solution is accurate and reliable as it is based on proven methods and formulas.

This digital product is intended for students and anyone studying physics and mathematics. Solution to problem 17.3.18 from the collection of Kepe O.?. will help you to better understand the topic related to mechanics and physics. Don't miss the opportunity to purchase this useful solution at a competitive price!

This product is a solution to problem 17.3.18 from the collection of Kepe O.?. in physics. The solution is intended for students and anyone studying physics and mathematics. In this solution you will find a detailed description of the steps required to solve the problem, calculations and formulas that will help you understand how we arrived at the answer.

The problem considers the rotation of a wheel of radius r = 0.2 m with angular acceleration ϵ = 20 rad/s2. The wheel is acted upon by a pair of forces with a moment M = 1.5 N m and a force T. The moment of inertia of the wheel relative to its axis of rotation is 0.05 kg m2. It is necessary to find the force modulus T.

The solution begins with determining the moment of forces acting on the wheel. The moment of forces is equal to the sum of the moments created by each of the forces: M = M1 + M2, where M1 is the moment of a pair of forces, M2 is the moment of force T. Using the formula M = I ε, where I is the moment of inertia of the object, and ε is its angular acceleration, we can write M1 + M2 = I·ε.

Next, substituting the known values, we obtain the equation: 1.5 N m + M2 = 0.05 kg m2 20 rad/s2. Solving it, we get the answer: the modulus of force T is equal to 2.5 N.

Thus, the solution to problem 17.3.18 from the collection of Kepe O.?. provides a detailed description of the steps and formulas required to solve a problem and is a useful resource for anyone studying physics and mathematics. After purchase, you will be able to download the solution file in PDF format and use it for your educational purposes.

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Solution to problem 17.3.18 from the collection of Kepe O.?. consists in determining the modulus of force T acting on a wheel of radius r = 0.2 m, which rotates with angular acceleration ϵ = 20 rad/s2. It is given that a pair of forces with a moment M = 1.5 N m acts on the wheel and the moment of inertia of the wheel relative to its axis of rotation is 0.05 kg m2.

To solve the problem, it is necessary to use the equation of rotational motion of a rigid body:

М = Iα,

where M is the moment of forces acting on the body, I is the moment of inertia of the body relative to its axis of rotation, α is the angular acceleration of the body.

Given this equation, we can express the force T acting on the wheel as follows:

T = (M - I*ϵ)/r,

where r is the radius of the wheel.

Substituting known values, we get:

T = (1.5 N m - 0.05 kg m2 20 rad/s2)/0.2 m = 2.5 N.

Thus, the modulus of force T acting on the wheel is 2.5 N.

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