ChloeYip said:Homework Statement
A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 5.00 kg ,while the balls each have mass 0.300 kg and can be treated as point masses.
Find the moment of inertia of this combination about an axis parallel to the bar and 0.500 m from it.
Homework Equations
Parallel axis theorem: Ip = Icm + Md^2
Icm = I = ML²/12 + 2 * mr²
3. The attempt
Ip = Icm + Md^2 ==> wrong
I = Md^2 ==> right
Why don't I need to add "Icm"?
Thanks.
ChloeYip said:Find the moment of inertia of this combination about an axis parallel to the bar and 0.500 m from it.
ChloeYip said:My teacher told me that when ever the axis isn't past though center of mass, we can use it...
Isn't it?
ChloeYip said:"Part A
Find the moment of inertia of this combination about an axis perpendicular to the bar through its center.
Express your answer with the appropriate units.
I = 2.27 kg⋅m2
Correct"I have calculated the Icm, and it is right...
ChloeYip said:Do you mean the axis of rotation (dimension) is different this time?
But why don't we need to calculate Icm in the required direction and then add Md^2?
Thanks
meaning no rotation?PeroK said:moment of inertia is 0
I understand this, that means answer in part a can't apply on this question. But, why don't we need to calculate Icm in the required direction for this question? (Let Icm pass through centre of mass and parallel to the bar)PeroK said:depends on the direction you rotate it
ChloeYip said:meaning no rotation?
I understand this, that means answer in part a can't apply on this question. But, why don't we need to calculate Icm in the required direction for this question? (Let Icm pass through centre of mass and parallel to the bar)
Huhh, no radius of the rod is given, do you mean it is assuming the radius of the rod is zero?
The Parallel Axis Theorem is a physics concept that relates to the moment of inertia of an object. It states that the moment of inertia of an object about a certain axis is equal to the moment of inertia of the object about a parallel axis through its center of mass, plus the product of the mass of the object and the square of the distance between the two axes.
The Parallel Axis Theorem is important because it allows us to calculate the moment of inertia of an object about any axis, not just the center of mass. This is useful in many physics and engineering applications, such as calculating the stability of rotating objects or designing structures that can withstand rotational forces.
The Parallel Axis Theorem can be derived using the moment of inertia of a continuous body formula, which involves integrating the mass of the object with respect to its distance from the axis of rotation. By manipulating this formula, we can arrive at the Parallel Axis Theorem.
The Parallel Axis Theorem can be seen in various real-world situations, such as a spinning top (where the moment of inertia changes as the axis of rotation moves away from the center) or a figure skater performing a spin (where they can change their moment of inertia by extending or contracting their arms).
While the Parallel Axis Theorem is a useful concept, it does have some limitations. It assumes that the object being rotated is rigid and has a constant mass distribution. It also does not take into account the effects of external forces on the object's moment of inertia.