Comparing Angular Velocity
On a merry-go-round of radius r, point A is a distance of r from the center while points B and C are distance r/2 from the center. How do their angular velocities compare? Since A is at twice the distance of B and C, the force on it is greater so it should be going faster, right?
Answer
First, start with a definition of angular velocity: the change in angle over the change in time. In other words, the angular velocity refers to how fast something is spinning. All three points make one full revolution (360 degrees) in the same amount of time, so their angular velocities must be the same.
An object on a merry-go-round travels in a circle and thus must have a centripetal force acting on it, which points radially inwards and keeps it going in a circle. The centripetal force is F = m r ω^2, where m is the mass, r is the radius, and ω is the angular speed. Like you said, A is at twice the distance of B and C so the force IS greater and it IS actually moving faster even though the angular speeds are the same!
To understand why, remember the relation between tangential velocity and angular velocity:
v = ωr
For the same angular speed, an object at a greater radius will have a faster tangential speed; it has a larger circumference to cover in the same amount of time! I hope this helps clear up the difference between velocity and angular velocity.
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First, start with a definition of angular velocity: the change in angle over the change in time. In other words, the angular velocity refers to how fast something is spinning. All three points make one full revolution (360 degrees) in the same amount of time, so their angular velocities must be the same.
An object on a merry-go-round travels in a circle and thus must have a centripetal force acting on it, which points radially inwards and keeps it going in a circle. The centripetal force is F = m r ω^2, where m is the mass, r is the radius, and ω is the angular speed. Like you said, A is at twice the distance of B and C so the force IS greater and it IS actually moving faster even though the angular speeds are the same!
To understand why, remember the relation between tangential velocity and angular velocity:
v = ωr
For the same angular speed, an object at a greater radius will have a faster tangential speed; it has a larger circumference to cover in the same amount of time! I hope this helps clear up the difference between velocity and angular velocity.