Can you explain the physics behind the pizza dough twirl & spin?

On a carousel - all of the animals travel at the same angular speed. What was the formula for angular speed? What if the animals could come off the base of the carousel and run? Would their motion be in a straight line or circular motion?

Relationships Between Angular and Linear Quantities Speed is same but direction is changing at every point tangent to the circle. (What is a tangent?) A line that touches a circle at only one point Tangential Speed (v t ) - the instantaneous linear speed of an object directed along the tangent to the object’s circular path.

Animals on a carousel move at the same angular speed (ω), but different tangential speeds (v t ). Tangential speed = distance from axis × angular speed Different radius = different v t Units for v t = m/s

The radius of a CD in a computer is m. If a microbe riding on the disc’s rim has a tangential speed of 1.88 m/s, what is the disc’s angular speed? Given: r = m v t = 1.88 m/s Unknown: ω = ?

Tangential Acceleration- the instantaneous linear acceleration of an object directed along the tangent to the object’s circular path. Tangential acceleration is tangent to the circular path. (linear) Units for a t = m/s 2 Tangential acceleration = distance from axis × angular acceleration

A spinning ride at a carnival has an angular acceleration of 0.50 rad/s 2. How far from the center is a rider who has a tangential acceleration of 3.3 m/s 2 ? Given: α = 0.50 rad/s 2 a t = 3.3 m/s 2 Unknown: r = ?

r = 1.5 m r = 0.51 m α = 0.63 rad/s 2

Centripetal Acceleration Centripetal Acceleration- acceleration directed toward the center of a circular path. Tangential and centripetal accelerations are perpendicular.

Centripetal Acceleration Although the car moves at a constant speed of 30 km/h, the car still has an acceleration because the direction of the velocity changes.

Centripetal acceleration = radius x (angular velocity) 2

A test car moves at a constant speed around a circular track. If the car is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s 2, what is its tangential speed? Given: r = 48.2 m a c = 8.05 m/s 2 Unknown: v t = ? VRRROMMM!!

Finding the Total Acceleration

v t = 2.5 m/s v t = 11 m/s v t = 1.5 m/s ω = 1.0 rad/s r = 58.7 m

Force maintains circular motion Inertia of object in motion wants to maintain straight-line path What is inertia? Force directed towards center of motion maintains circular path 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.

So NOW can you explain the pizza dough “spin secret”?