A solid disk and a hollow cylinder of the same mass and radius roll down an incl

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Question: A solid disk and a hollow cylinder of the same mass and radius roll down an incline. Which one reaches the bottom first?

Options:

Correct Answer: Solid disk

Solution:

The solid disk has a lower moment of inertia than the hollow cylinder, allowing it to accelerate faster down the incline.

A solid disk and a hollow cylinder of the same mass and radius roll down an incline. Which one reaches the bottom first?

A solid disk and a hollow cylinder of the same mass and radius roll down an incline. Which one reaches the bottom first?

Step 1: Understand that both the solid disk and the hollow cylinder have the same mass and radius.
Step 2: Learn about moment of inertia, which is a measure of how difficult it is to change the rotation of an object.
Step 3: Know that the solid disk has a lower moment of inertia compared to the hollow cylinder.
Step 4: Realize that a lower moment of inertia means the solid disk can rotate more easily.
Step 5: Understand that when both objects roll down the incline, the one with the lower moment of inertia will accelerate faster.
Step 6: Conclude that the solid disk will reach the bottom of the incline before the hollow cylinder.

Moment of Inertia – The solid disk has a lower moment of inertia compared to the hollow cylinder, which affects how quickly it can roll down an incline.
Rolling Motion – Understanding the relationship between translational and rotational motion is crucial in determining which object accelerates faster.
Energy Conservation – The conversion of potential energy to kinetic energy (both translational and rotational) plays a key role in the dynamics of rolling objects.