Two small weights of mass 5.0 kg and 7.0 kg, are mounted 4.0 m apart on a light rod (whose mass can be ignored), as shown in the accompanying figure. Calculate the moment of inertia of the system
(a) when rotated about an axis halfway between the weights, and
(b) when rotated about an axis 0.50 m to the left of the 5.0 kg mass.

Question

Physics

Answered

Two small weights of mass 5.0 kg and 7.0 kg, are mounted 4.0 m apart on a light rod (whose mass can be ignored), as shown in the accompanying figure. Calculate the moment of inertia of the system
(a) when rotated about an axis halfway between the weights, and
(b) when rotated about an axis 0.50 m to the left of the 5.0 kg mass.

Sagot :

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INDRAWBOYIN INDRAWBOYIN · Answer 1

a. I = 48 kg.m²

b. I = 87 kg.m²

Further explanation

The moment of inertia is a measure of the inertia of an object to rotate on its axis.

Factors affecting moment of inertia:

The mass of objects
form
rotary axis
moment arm

Can be formulated :

[tex]\tt I=m\times R^2[/tex]

m is the mass of particle/object (kg)

R is the distance between the particle or mass of the object against the rotary axis (m)

I = ∑mₙRₙ²

The moment of inertia of the object is the sum of all the moments of inertia of the object's particles :

Given

mass 5.0 kg and 7.0 kg

4.0 m apart

Required

the moment of inertia

Solution

a. R₁=R₂=2 m( halfway between the weights)

I = (m₁+m₂)R²

I = (5+7)2²

I = 48 kg.m²

b. 0.50 m to the left of the 5.0 kg mass.

R₁(5 kg) = 0.5 m

R₂(7 kg) = 4 - 0.5 = 3.5 m

I = 5 x 0.5² + 7 x 3.5²

I = 1.25 + 85.75

I = 87 kg.m²

Learn more

An example of The Moment of Intertia

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Inertia

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the relationship of the mass of an object and inertia

https://brainly.ph/question/132731

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