Angular velocity is a measure of how quickly an object rotates or spins around a central point or axis. In this context of the bicycle wheel, it describes how fast the wheel is spinning. It is a vector quantity, meaning it has both a magnitude and a direction, but in most simple scenarios such as a bicycle wheel, we focus primarily on the magnitude.
Angular velocity is often represented by the Greek letter omega (\( \omega \)), and it is measured in radians per second (rad/s). Imagine it like the speed of a car, but for a rotating object instead. When a wheel spins faster, its angular velocity increases.
To calculate angular velocity when angular acceleration is constant, you use this equation:
\[ \omega = \omega_0 + \alpha t \]
Where:
- \( \omega_0 \) is the initial angular velocity (how fast it was spinning to begin with)
- \( \alpha \) is the angular acceleration
- \( t \) is the time elapsed
In the original problem, when the bicycle wheel started with an angular velocity of 1.50 rad/s and an angular acceleration of 0.200 rad/s² was applied for 2.5 seconds, its final angular velocity increased to 2.00 rad/s as calculated using the formula. This indicates the wheel spins faster over time due to the constant acceleration.