When a wheel is subject to constant angular acceleration, how does its angular velocity change?

When a wheel experiences constant angular acceleration, its angular velocity changes in a predictable manner. Angular acceleration is defined as the rate of change of angular velocity over time. When acceleration is constant, it means that the increase in angular velocity remains uniform over each time interval.

This leads to a linear increase in angular velocity. For example, if a wheel starts from rest and is subjected to a constant angular acceleration, after the first second, its angular velocity will have increased by a certain amount. After the second second, it will have increased by the same amount again, leading to a continuous and consistent growth in angular velocity. The relationship can be represented by the equation:

[

\omega_f = \omega_i + \alpha t

]

where (\omega_f) is the final angular velocity, (\omega_i) is the initial angular velocity, (\alpha) is the angular acceleration, and (t) is the time elapsed. This equation clearly shows that as time increases, the final angular velocity increases linearly based on the constant angular acceleration.

In summary, when subjected to constant angular acceleration, the wheel's angular velocity indeed increases in a linear fashion.