Why is a fan bald spinning at a constant speed constantly accelerating
Answered on
A fan blade spinning at a constant speed is constantly accelerating because acceleration is not just about changes in speed; it's also about changes in direction. When an object is moving in a circular path at a constant speed, its direction is constantly changing. This changing direction constitutes a change in velocity.
From the perspective of physics, velocity is a vector quantity, meaning it has both magnitude (speed) and direction. When an object moves in a circle, even if the speed (magnitude of the velocity vector) is constant, the direction of the velocity vector is always changing.
Acceleration is defined as the rate of change of velocity. So, because the direction of the velocity vector is changing at each point along the circular path, the fan blade experiences a centripetal (center-seeking) acceleration that is always perpendicular to the velocity vector and points towards the center of the circle.
This centripetal acceleration is what keeps the fan blade moving in a circular path, and is given by the equation:
a = v^2 / r
where a is the centripetal acceleration, v is the speed of the fan blade, and r is the radius of the circular path.
So despite the constant speed of the fan blades, they are experiencing a constant centripetal acceleration toward the center of the fan.