A disk rolls down a slope of height h. What fraction of its total energy is tran

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Question: A disk rolls down a slope of height h. What fraction of its total energy is translational at the bottom?

Options:

Correct Answer: 2/3

Solution:

At the bottom, the total energy is converted into translational and rotational energy. The translational energy is 2/3 of the total energy.

A disk rolls down a slope of height h. What fraction of its total energy is translational at the bottom?

A disk rolls down a slope of height h. What fraction of its total energy is translational at the bottom?

Step 1: Understand that the disk starts at a height 'h' and has potential energy due to its height.
Step 2: Recognize that as the disk rolls down the slope, this potential energy converts into two types of energy: translational energy (movement) and rotational energy (spinning).
Step 3: Know that the total energy at the bottom of the slope is equal to the initial potential energy at height 'h'.
Step 4: Realize that for a rolling disk, the relationship between translational energy and total energy is given by the formula: Translational Energy = (2/3) * Total Energy.
Step 5: Conclude that at the bottom of the slope, the fraction of the total energy that is translational is 2/3.

Conservation of Energy – The principle that the total energy in a closed system remains constant, allowing for the conversion between potential, translational, and rotational energy.
Moment of Inertia – The distribution of mass in a rotating object, which affects how much of the total energy is translational versus rotational.
Rolling Motion – The combination of translational and rotational motion that occurs when an object rolls without slipping.