Angular Displacement and Speed Rotational Motion Angular Displacement and Speed HMH Physics Chapter 7 pages 224-269 Section 1 pages 226-231

Convert angle measurements between degrees and radians. Explain the right hand rule and vector direction of circular motion. Calculate Arc length traveled during circular motion. Calculate Angular Speed.

Rotational Quantities Rotational motion the motion when an object spins Circular motion is described in terms of the angle

s r the distance measured along the circumference of a circle Θ = the angle s = the arc length in meters the distance measured along the circumference of a circle r = the length of the radius in meters (distance of the object from the axis of rotation) s Θ r

Angles are often measured in radians in science An angle in radians is the ratio of the arc length to the radius s Θ = --- r Θ has no units, but we use the abbreviation rad when the angle is measured in radians

One revolution in a circle is 360˚, which is equal to 2Π rad 1 turn or revolution = 2 rad

You can use this formula to convert an angle in degrees to an angle in radians (or some calculators have a function to convert for you) Π Θ (rad) = --- Θ (deg) 180˚

Angular displacement describes how much an object has rotated It is the change in the arc length, Δs, divided by the distance of the object from the axis of rotation, r Δs ΔΘ = --- r

When an object rotates counterclockwise, the arc length, s, and angular displacement, ΔΘ, are considered positive When an object rotates clockwise, the arc length, s, and angular displacement, ΔΘ, are considered negative + -

While riding a carousel that is rotating clockwise, a child travels through an arc length of 11.5 m. If the child’s angular displacement is 165˚, what is the radius of the carousel?

ωavg = ---- units = rad/s Angular speed describes rate of revolution It is the ratio of the angular displacement to the time interval ΔΘ ωavg = ---- units = rad/s Δt Similar to the linear equation for velocity: Δx Vavg = ---

A child at an ice cream parlor spins on a stool A child at an ice cream parlor spins on a stool. The child turns counterclockwise with an average angular speed of 4.0 rad/s. In what time interval will the child’s feet have an angular displacement of 8.0Π rad?