Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed?
Angular speed is a measure of how quickly an object is rotating around a fixed axis. It is defined as the change in angular displacement per unit of time. In this case, child A is at a greater distance from the axis of rotation than child B.
Since both children are riding on the same merry-go-round, which has a fixed axis of rotation, they have the same period of rotation. The period is the time it takes for one complete revolution.
Child A, being farther from the axis of rotation, travels a larger distance in the same period compared to child B. If they both complete one revolution (360 degrees) in the same time, child A has a larger angular distance to cover, which means child A has a larger angular speed.
Therefore, child A has a larger angular speed than child B.
To determine which child has the larger angular speed, we need to understand what angular speed is. Angular speed is a measure of how quickly an object rotates or turns around a fixed point. It is defined as the rate at which an object changes its angle relative to a reference point.
In this case, the merry-go-round is rotating around an axis, and each child is at a different distance from this axis. Imagine Child A is located farther from the axis compared to Child B.
Angular speed is calculated by dividing the angle displaced by an object by the time it takes to complete that displacement. Since both children complete one full rotation around the merry-go-round, they both displace the same angle.
However, since Child A is further from the axis, they have to travel a greater distance to complete one revolution compared to Child B. This means that Child A covers a larger arc length while rotating.
Since the angular displacement is the same for both children, but Child A covers a greater distance in the same amount of time, it means that Child A has a larger linear speed.
Angular speed is defined as the linear speed divided by the radius. Since linear speed is higher for Child A, and both children are rotating in equal time intervals, it means that Child A has a larger angular speed.