Moment of inertia of solid slab

In summary, the problem involves a solid slab with a moment of inertia of 2 kg m2 and given forces, where the goal is to find the angular acceleration when θ = 37°, R1 = 10 cm, and R2 = 25 cm. The solution involves finding all the torques by the 4 forces, with τ1 = 10 x R2 (clockwise), τ2 = 10 x R1 (anti-clockwise), and τ3 = 20 x R1 (anti-clockwise). The fourth torque cannot be found due to the lack of information on the perpendicular distance from the inclined-10 N force to the center. Suggestions are given to resolve the force into 2 components:
  • #1
songoku
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Homework Statement


Solid slab with moment of inertia 2 kg m2 is given the forces as shown.
1-1.jpg


Find the angular acceleration if θ = 37°, R1 = 10 cm, R2 = 25 cm

Homework Equations


τ = I . α

The Attempt at a Solution


This is what I've tried although I don't know it is correct or wrong; I tried to find all the torques by the 4 forces.
τ1 = 10 x R2 (clockwise)
τ2 = 10 x R1 (anti-clockwise)
τ3 = 20 x R1 (anti-clockwise)

I can't find the fourth torque because I don't know how to find the perpendicular distance from the inclined-10 N force to the center. Please help

Thanks
 
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  • #2
Hint: You can resolve it into 2 components: tangential and radial
 
  • #3
cupid.callin said:
Hint: You can resolve it into 2 components: tangential and radial

Sorry I don't get it. The arrow of the force is "toward" the slab, not "away" from it so if I resolve the force, I will get 10 cos θ and 10 sin θ but I don't see that one of them is tangential and one of them is radial.
 
  • #4
songoku said:
Sorry I don't get it. The arrow of the force is "toward" the slab, not "away" from it so if I resolve the force, I will get 10 cos θ and 10 sin θ but I don't see that one of them is tangential and one of them is radial.

You are right, one of them won't actually be radial

attachment.php?attachmentid=42453&stc=1&d=1325703328.jpg


But since the blue distance is no given so i assume that its the imperfection of the figure causing the problem.
If you have a way of finding the blue distance the its good or else IMO you can call it radial ...
 

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  • #5
cupid.callin said:
You are right, one of them won't actually be radial

attachment.php?attachmentid=42453&stc=1&d=1325703328.jpg


But since the blue distance is no given so i assume that its the imperfection of the figure causing the problem.
If you have a way of finding the blue distance the its good or else IMO you can call it radial ...

OK I think I get it. Thanks for your help :)
 

FAQ: Moment of inertia of solid slab

What is moment of inertia of a solid slab?

Moment of inertia of a solid slab is a physical property that measures the resistance of the object to changes in its rotational motion. It is also known as rotational inertia and is an important factor in understanding how objects behave when subjected to a torque or rotational force.

How is moment of inertia of a solid slab calculated?

The moment of inertia of a solid slab can be calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. The formula for calculating moment of inertia is I = mr², where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation.

Why is moment of inertia important?

Moment of inertia is important because it helps us understand how an object will respond to a torque or rotational force. It is also used in various engineering and physics applications, such as designing structures that can withstand rotational forces or predicting the behavior of spinning objects.

How does the moment of inertia of a solid slab differ from other shapes?

The moment of inertia of a solid slab is different from other shapes because the distribution of mass is different. For example, a solid cylinder has a larger moment of inertia than a solid sphere of the same mass, as more of its mass is located farther from the axis of rotation.

What factors can affect the moment of inertia of a solid slab?

The moment of inertia of a solid slab can be affected by several factors, including the shape of the object, the mass of the object, and the distance of the object from the axis of rotation. The moment of inertia can also be affected by the material properties of the object, such as density and distribution of mass.

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