Rotational Motion and the Law of Gravity Measuring Rotational Motion

Rotational Quantities Rotational motion – the motion of an object that spins about an axis When an object spins Axis of rotation – the line about which the rotation occurs Circular motion – when an object spins around a single axis Arc length – the distance an object moves around the circumference of the circle

Rotational Quantities Radian – an angle whose arc length is equal to its radius, which is approximately equal to 57.3o Angular displacement – how much an object has rotated Measured in radians (rad)

Rotational Quantities Angular displacement (in radians) = the change in arc length/the length of the radius Δθ=Δs/r Δθ is positive for counterclockwise rotation and negative for clockwise rotation

Rotational Quantities

Rotational Quantities Angular speed – rate of rotation Measured in radians per second (rad/s) Sometimes measured in revolutions per unit of time, such as seconds (rev/s) or minutes (rev/min or RPM’s) Represented by the lowercase Greek letter omega (ω) Some times called average angular speed (ωavg) Average angular speed = angular displacement/time interval ωavg= Δθ/Δt

Rotational Quantities Angular acceleration occurs when angular speed changes Measured in radians per second2 (rad/s2) Represented by the lowercase Greek letter alpha (α) Average angular acceleration = change in angular speed/time interval αavg = (ω2- ω1)/(t2-t1) = Δω/Δt All points on a rotating rigid object have the same angular acceleration and angular speed

Comparing Angular and Linear Quantities Every angular quantity matches up with a corresponding linear quantity θ matches up with x ω matches up with v α matches up with a We have a series of equations for rotational motion with constant angular acceleration

Comparing Angular and Linear Quantities