A flywheel rotates about an axis. Due to friction at the axis, it experiences an angular retardation proportional to its angular velocity. If its angular velocity falls to half while it makes `n` rotations, how many more rotations will it make before coming to rest?

Options

A. `2n`
B. `n`
C. `(n)/(2)`
D. `(n)/(3)`

Explanation

To solve the problem step by step, we will analyze the motion of the flywheel under the influence of angular retardation proportional to its angular velocity.

### Step 1: Set up the relationship between angular velocity and angular displacement
Given that the angular retardation (α) is proportional to the angular velocity (ω), we can express this as:
\[ \alpha = -k \omega \]
where \( k \) is a positive constant of proportionality.
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