At a given rotational speed, how does linear speed change as the distance from the axis changes?
tangential speed= radius*angular velocity
To understand how linear speed changes as the distance from the axis changes, we need to consider the concept of rotational motion and the relationship between linear speed and rotational speed.
In rotational motion, an object rotates around an axis, commonly referred to as the center of rotation. Linear speed, also known as tangential speed, refers to the speed of an object at a given point on its circular path. It represents the distance traveled per unit of time along the circular path.
The relationship between linear speed (v) and rotational speed (ω) is given by the equation:
v = r * ω
where:
- v is the linear speed
- r is the distance from the axis (radius)
- ω is the rotational speed or angular velocity
According to this equation, linear speed is directly proportional to the distance from the axis (r) and the rotational speed (ω). When the distance from the axis increases, the linear speed also increases, assuming the rotational speed remains constant.
Conversely, if the distance from the axis decreases, the linear speed will decrease, assuming the rotational speed remains the same. This relationship shows that a point located farther from the axis will move with a greater linear speed compared to a point closer to the axis when both are rotating at the same speed.
So, in summary, as the distance from the axis changes, linear speed changes proportionally, as long as the rotational speed remains constant.