A toy train runs on a circular track of radius 2 m. The train moves 2 m along the track's edge: exactly one radius-length of travel.
Degrees are not the only way to measure the swept angle. The circle offers a natural angle of its own.
The distance measured along the circle's edge is called the arc length.
The train's arc length here is 2 m, and the circle's radius is also 2 m.
The radian uses the circle's own radius as its measuring stick.
Each further radius-length of arc sweeps one more radian: a 4 m arc on this circle sweeps 2 radians.
The circle's whole edge is 2π radii long, because the circumference is 2π times the radius.
So one full turn sweeps 2π radians, which is about 6.28 radians.
The count of radians does not depend on the circle's size: a bigger circle has a longer edge, but its measuring stick, the radius, grows to match.
On a circular track of radius 5.0 m, a robot vacuum moves 15 m along the edge. Enter the swept angle in radians.
Dagny says: 'On a circle of radius 9 m, moving 9 m along the edge sweeps an angle of one radian.' Is Dagny correct?
On a circle of radius 6.0 m, an object moves 6.0 m along the edge. State the swept angle.
The arc length, 6.0 m, equals the radius, 6.0 m.
The swept angle is 1 radian.
On the same circle of radius 6.0 m, the object moves 12 m along the edge. State the swept angle.
The arc is two radius-lengths: 12 m is two lots of 6.0 m.
Each radius-length of arc sweeps one radian.
The swept angle is 2 radians.
A remote-control car drives a circle of radius 1.6 m, traveling 12.8 m along it. Enter the swept angle in radians.
A circle has a radius of 7 m. Which move sweeps an angle of exactly 1 radian?
Which statement about radians is correct?
When the distance moved along a circle's edge equals the circle's radius, the swept angle is called one ___.