It feels like we’re going in circles…

Rotational motion = object spinning around an axis

Any single point moves in a circular path around the axis at a distance r (radius) from the center

How do you determine the distance traveled?◦Choose reference line where t = 0◦After ∆t, point has moved to new position◦= with respect to start◦Distance between start/stop = arc length

(s)

Angular displacement

deg)1 revolution around the

circle = 1 rev = 2πrad

To convert from degrees to radians:Multiply the number of degrees by

π/180.Example: Express 135° in radians.

= rad

To convert from radians to degrees:Multiply the number of radians by

180°/π. Example: Express as 8π/3 degrees.

480◦

p. 247

Let’s kick it up a notchWhat is the formula to find speed?

◦Speed = distance/timeAngular speed = angular

displacement/time◦How fast you are going around the circle

Rad/s(remember 1 rev = 2πrad)

Gaining speedWhat is acceleration?

◦Acceleration = change in speed/timeAngular acceleration = change in

angular speed/time◦How fast are you changing speeds

around the circle.

=

Angular substitutes for linear quantities

Linear Angularx thetav omegaa alpha

Linear motion w/constant acceleration

Rotational motion w/constant angular acceleration

Are you still here?!

Stop the slide – I’m getting dizzy!

Unbelievable!

Without a centripetal force, an object in motion continues along

a straight-line path.

With a centripetal force, an object in motion will be accelerated and

change its direction.

Relationships Between Angular and Linear Quantities

Tangential Speed - the instantaneous linear speed of an object directed along the tangent to the object’s circular path.