Circular / rotational motion

You figure it out… Do the ‘spinning disk’ activity What’s the difference between Linear speed/ velocity? Angular/rotational speed/velocity? Do the ‘quarter and coin’ activity Rotation and Revolution?

Rotation is…. Circular motion around an object’s internal axis Around a point inside the object Example: Earth on its own axis CD, DVD, record Ice skater in a spin

Revolution is… Circular motion around an external axis Examples: a point outside of the object Examples: earth around the sun (ok it’s elliptical) Child on a merry-go-round

What about different points on the same rotating object? Every point on the object undergoes circular motion about the point O All parts of the object of the body rotate through the same angle during the same time The object is considered to be a rigid body This means that each part of the body is fixed in position relative to all other parts of the body REMEMBER THE DOTS ON THE LAZY SUSAN DISK? Like kids on a merry-go-round!

Describing circular motion Linear speed/velocity - the (arc length) distance moved per unit time. Angular/rotational speed/velocity - the number of degree, radians, or revolutions per unit time. How can we measure the above for a spinning disk?

Angular speed in revolutions/sec Easy! Start timer Count a predetermined # of complete revolutions Stop timer Divide # rev/ measured time Angular speed in rev/sec is the reciprocal of the period T

T = 1 / f f = 1 / T Period and Frequency The Period (T) of a body travelling in a circle at constant speed is time taken to complete one revolution - measured in seconds Frequency (f) is the number of revolutions per second – measured in Hz In circular motion aka angular/rotational speed T = 1 / f f = 1 / T

How to calculate linear speed? Identify the radial position, r = ?? Calculate the circumference of the circular path 2πr Multiply (2πr) x (#rev) to get total distance Divide by total time Another way Linear speed v = 2πr / T = circumference / period

Various Units for displacement and angular speed Degrees, radians, revs / sec 1 radian =~ 57º 2π = 6.28 radians in a whole circle 360 degrees = 2π radians = 1 circumference or rev. = 2πr in linear distance

If Angular speed is in radians/sec… Angular speed ω is the angle turned through per second ω = θ/t = 2π / T 2π = whole circle angle T = time to complete one revolution So what’s the mathematical relationship between linear and angular speed?

Relationship Between Angular and Linear Quantities Displacements Speeds Every point on the rotating object has the same angular motion Every point on the rotating object does not have the same linear motion

Example On a merry-go-round the horses on the outer rail are located 2 times as far from the horses on the inside rail. If a girl sits on a horse on the inside rail at a rotational speed of 3 RPM and a linear speed of 2 m/s, what will be the rotational speed and linear speed of her brother who is on a horse on the outer rail? His rotational speed: the same at 3 RPM. His linear speed: 2 times faster or 2 x 2 = 4 m/s.

Practice problem solving Circular motion worksheet Our first problems will deal with describing motion Objects that are rotating Objects that are sitting on /attached to rotating objects Next topic: why do objects move in circular motion? Think Newton’s laws…..