Dagny rides a Ferris wheel. Her seat goes a quarter of the way around the wheel.
How far around is that, exactly?
Earlier in the course you saw displacement: how far an object's position changed.
Angular displacement is the same idea for turning: how far around the object has swept.
Draw the line from the wheel's center to Dagny's seat.
As the wheel turns, that line sweeps out an angle.
A quarter of the way around sweeps 90°.
Half of the way around sweeps 180°, and the whole way around sweeps 360°.
A merry-go-round carries a rider three quarters of the way around. Enter the rider's angular displacement in degrees.
Coral says: 'A rider who goes all the way around once sweeps an angular displacement of 360°.' Is Coral correct?
The angle measures the turn itself. It does not depend on how big the circle is.
A merry-go-round carries a rider half of the way around. State the rider's angular displacement.
The line from the center to the rider sweeps half of a full turn.
Half of 360° is 180°.
The rider's angular displacement is 180°.
A ceiling fan blade turns exactly once around. State the blade's angular displacement.
The line from the hub to the blade tip sweeps one full turn.
One full turn is 360°.
The blade's angular displacement is 360°.
A Ferris wheel seat goes one and a half times around the wheel. Enter the seat's total angular displacement in degrees.
A cart rides a circular track. Which angle is the cart's angular displacement?
Two riders sit on one carousel, one 2 m from the center and one 4 m out. The carousel turns a third of the way around. Which statement is correct?
The angle swept out by the line from the circle's center to a moving object is called the object's ___.