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

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 pointTangential Speed (vt) - 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 (vt).

rvtTangential speed =

distance from axis × angular speed

Different radius = different vt

Units for vt = m/s

The radius of a CD in a computer is 0.0600 m. If a microbe riding on thedisc’s rim has a tangential speed of 1.88 m/s, what is the disc’s angular speed?

Given:r = 0.0600 mvt = 1.88 m/s

Unknown: ω = ?

srad

sm

3.31m 0600.0

88.1

r

vt

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 at = m/s2

rat

Tangential acceleration =

distance from axis × angular acceleration

A spinning ride at a carnival has an angular acceleration of 0.50 rad/s2. How far from the center is a rider who has a tangential acceleration of 3.3 m/s2?

Given:α = 0.50 rad/s2

at = 3.3 m/s2

Unknown: r = ? m 6.6

.500

3.3

2

2

srad

sm

r

r

ar t

r = 1.5 m

r = 0.51 m

α = 0.63 rad/s2

Centripetal AccelerationCentripetal 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.

2

2

ra

r

va

c

tc

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/s2, what is its tangential speed?

Given:r = 48.2 mac = 8.05 m/s2

Unknown: vt = ? VRRROMMM!!

Finding the Total Acceleration

vt = 2.5 m/s

vt = 11 m/s

vt = 1.5 m/sω = 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”?