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babymother [125]
3 years ago
10

The parallel axis theorem relates Icm, the moment of inertia of an object about an axis passing through its center of mass, to I

p, the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is Ip=Icm+Md², where d is the perpendicular distance from the center of mass to the axis that passes through point p, and M is the mass of the object.Part A Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by Icm=112mL². Find Iend, the moment of inertia of the rod with respect to a parallel axis through one end of the rod. Express Iend in terms of m and L. Use fractions rather than decimal numbers in your answer. Part B Now consider a cube of mass m with edges of length a. The moment of inertia Icm of the cube about an axis through its center of mass and perpendicular to one of its faces is given by Icm=16ma². Find Iedge, the moment of inertia about an axis p through one of the edges of the cube Express Iedge in terms of m and a. Use fractions rather than decimal numbers in your answer.
Physics
1 answer:
erma4kov [3.2K]3 years ago
7 0

Answer:

Part a)

I_{end} = \frac{mL^2}{3}

Part b)

I_{edge} = \frac{2ma^2}{3}

Explanation:

As we know that by parallel axis theorem we will have

I_p = I_{cm} + Md^2

Part a)

here we know that for a stick the moment of inertia for an axis passing through its COM is given as

I = \frac{mL^2}{12}

now if we need to find the inertia from its end then we will have

I_{end} = I_{cm} + Md^2

I_{end} = \frac{mL^2}{12} + m(\frac{L}{2})^2

I_{end} = \frac{mL^2}{3}

Part b)

here we know that for a cube the moment of inertia for an axis passing through its COM is given as

I = \frac{ma^2}{6}

now if we need to find the inertia about an axis passing through its edge

I_{edge} = I_{cm} + Md^2

I_{edge} = \frac{ma^2}{6} + m(\frac{a}{\sqrt2})^2

I_{edge} = \frac{2ma^2}{3}

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A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical axis through its center. A 68.
Andreyy89

Answer:

I_{total}=220.64 kg*m^{2}

Explanation:

The moment of inertia of the system is equal to the each population and the platform inertia so

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I_{disk}=\frac{1}{2}*m_{disk}*(r_{p})^{2}

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I_{p}=\frac{1}{2}*m_{p}*(r_{p})^{2}

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The Inertia of the system is the sum of each mass taking into account that all exert the force of inertia:

I_{total}=I_{disk}+I_{p}+I_{d}

I_{total}=\frac{1}{2}*103kg*(1.71)^{2}+\frac{1}{2}*68.9kg*(1.09)^{2}+\frac{1}{2}*27.7kg*(1.45)^{2}

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5 0
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A 75kg man climbs the stairs to the fifth floor of a building. A total hieght of 16m. His potential energy has increased by
yKpoI14uk [10]

Answer:

11760 joules

Explanation:

Given

Mass (m) = 75kg

Height (h) = 16m

Required

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Where g = 9.8m/s²

Substitute values for m, g and h.

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As we know that the right-hand rule is based on the relation of magnetic fields and the forces that they exert on moving charges.When a charged particle moves under a magnetic field, it exerts a force on the particle, which is not in the same direction but different than the direction of the magnetic field.Under the right-hand rule,  if we point our pointer finger in the direction of the charged particle is moving and the middle finger is representing the direction of the magnetic field then our thumb depicts the direction of the magnetic force which is exerted on the charged particle.

So,  we are given that the direction of the velocity of the proton is in the negative y direction and the direction of the magnetic field is in the positive x  direction,  so the magnetic force is acting in the positive z direction.

To know  more about the right-hand rule refer to the link brainly.com/question/9750730?referrer=searchResults.

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