Dynamics question regarding moment of inertia

In summary, the conversation discusses a question on dynamics involving finding angular acceleration, frictional force, and acceleration of G. The equations used were ƩFx, ƩFy, and ƩMG, with the values for friction force and acceleration of G being correct but the angular acceleration being wrong. The values for ΔFf, Ag, and α were also given, with a question about the use of cos(30) in the equation.
  • #1
chicagobears34
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Hi, I have a question regarding a dynamics question that be found here:http://by.genie.uottawa.ca/~mess/files/MCG_2107/MCG2107_M2005_p2.pdf, It is the first problem on that link (labeled number 2.)

I did ƩFx, ƩFy, ƩMG which allowed me to find angular acceleration, frictional force, and acceleration of G.
Friction force and acceleration of G were correct but angular acceleration was wrong.
My equations were:
ƩFx: -μkN + T cos(30)=maG
ƩFy: N-mg+Tsin(30)=0
ƩMG: Tcos(30)(0.075)-μkN(0.2)=Iα
ΔFf=17.6N, Ag=1.0281, α=8.84
α should be equal to .295
 
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  • #2
hi chicagobears34! :smile:
chicagobears34 said:
ƩMG: Tcos(30)(0.075)-μkN(0.2)=Iα

why cos(30) ? :wink:
 
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Related to Dynamics question regarding moment of inertia

1. What is moment of inertia and how is it calculated?

Moment of inertia is the measure of an object's resistance to rotational motion. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

2. What factors affect the moment of inertia of an object?

The moment of inertia of an object depends on its mass, shape, and distribution of mass around the axis of rotation. Objects with more mass or a larger distance from the axis will have a greater moment of inertia.

3. How does the moment of inertia affect the dynamics of an object?

The moment of inertia affects an object's rotational motion by determining how much torque is needed to produce a certain angular acceleration. Objects with a higher moment of inertia will require more torque to rotate.

4. How is the moment of inertia different from mass?

Mass is a measure of an object's resistance to linear motion, while moment of inertia is a measure of its resistance to rotational motion. Mass is a scalar quantity while moment of inertia is a tensor quantity.

5. Can the moment of inertia be changed?

Yes, the moment of inertia can be changed by altering the mass, shape, or distribution of an object's mass. For example, by moving mass closer to or further from the axis of rotation, the moment of inertia can be increased or decreased.

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