what is the velocity at the top most point when a object is moving in a ciircular path
When an object is moving in a circular path, the velocity at the topmost point of the path can be analyzed in the context of uniform circular motion. Here's a breakdown:
1. **Definition of Velocity in Circular Motion**: Velocity in circular motion is always tangential to the path. This means the speed is constant if the motion is uniform, but the direction of velocity changes continuously.
2. **Topmost Point in Circular Motion**: At the topmost point of a vertical circular path, gravity acts downward while the centripetal force needed to keep the object in circular motion also acts downward. The net force acting on the object provides the centripetal force required for circular motion.
3. **Expression for Velocity**: The centripetal force \(F_c\) required to keep the object moving in a circle of radius \(r\) with velocity \(v\) is given by:
\[
F_c = \frac{mv^2}{r}
\]
At the topmost point, the gravitational force \(mg\) helps provide the centripetal force, so:
\[
mg + N = \frac{mv^2}{r}
\]
where \(N\) is the normal force at the topmost point. For an object just moving in the circle (minimal normal force), \(N\) can be approximated as zero:
\[
mg = \frac{mv^2}{r}
\]
Solving for \(v\):
\[
v = \sqrt{gr}
\]
In summary, at the topmost point of a vertical circular path, the velocity \(v\) can be found using \(v = \sqrt{gr}\), where \(g\) is the acceleration due to gravity and \(r\) is the radius of the circle.
