AP Physics 1 Physics — practice by topic

1. A rotation angle of two pi radians corresponds to an object returning to its starting position after tracing the full circumference, which is one complete revolution. 2. Because the arc length of a full circle is the circumference 2 pi r, dividing by the radius r gives a rotation angle of exactly 2 pi radians for one revolution. 3. Pi radians describes only a half turn, not a full revolution. 4. 360 radians and one radian each describe an amount of rotation far removed from a single full turn, since 360 degrees, not 360 radians, equals one revolution. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.1 Rotation Angle and Angular Velocity_

1. Angular velocity is defined as the rate of change of the rotation angle, the angle swept divided by the time taken. 2. The radius of the path is a fixed geometric property of the circle, not a rate of change, so it cannot be the angular velocity. 3. Linear speed at the rim is related to angular velocity through v equals r times omega, but it is a distinct quantity measured in meters per second rather than radians per second. 4. Centripetal acceleration is built from angular velocity and radius, not the rate of change of angle itself. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.1 Rotation Angle and Angular Velocity_

1. Because the tire rolls without slipping, the tire rim's linear speed equals the car's speed, so v = 15.0 m/s. 2. Angular velocity is omega = v / r. 3. Substituting the known values, omega = 15.0 m/s / 0.300 m. 4. That division gives omega = 50.0 rad/s. 5. 12.5 rad/s is the value for a much larger 1.20 m tire at the same speed, and 45.0 rad/s and 5.00 rad/s come from arithmetic slips in the division. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.1 Rotation Angle and Angular Velocity_