Rotational Inertia: Mass Distribution & Rolling Object Comparison

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Rotational inertia is influenced by both mass and its distribution relative to the axis of rotation. A hoop, with all its mass at a fixed distance, has a higher rotational inertia compared to a solid sphere of the same mass, which has mass distributed closer to the axis. This distribution means that the sphere experiences lower resistance to angular acceleration. Consequently, when rolled, the solid sphere accelerates more easily than the hoop. Understanding these principles is crucial for analyzing the motion of rolling objects.
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The Rotational inertia of an object depends not on the mass alone but on the distribution of the mass. Between a hoop and a solid sphere of the same mass which object has higher rotational inertia when they are rolled? Explain how the distribution of the mass affects rotational inertial.
 
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Intuitively, the further away the mass is from the axis of rotation, the higher the moment of inertia.
In a hoop all the mass is distributed at a fixed distance.
In a sphere there is mass closer to the axis of rotation (assuming it has the same radius as the hoop), so its moment of inertia will be lower.
 
Thank you that helps a lot...
 
RPDuece said:
Help with this problem...

The Rotational inertia of an object depends not on the mass alone but on the distribution of the mass. Between a hoop and a solid sphere of the same mass which object has higher rotational inertia when they are rolled? Explain how the distribution of the mass affects rotational inertial.
The elements of matter contained in rigid body experiencing angular acceleration (ie. a torque acting on it) have different accelerations depending on their distance from the centre of rotation (centre of mass). The mass that is farther from the centre is accelerated more rapidly than mass closer to the centre. So to determine what angular acceleration results from a given torque, one has to compute the rotational inertia of the body, which depends on the distribution of mass in relation to the centre of mass.

AM
 

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