NATURAL RHYTHMS ACTIVITYCycle, Period (T), and Frequency (f)

4 minutes

TIME’S UP!!!

3 minutes

2 minutes

1 minutes

30 seconds

15 seconds

Basic Definitions• How are T and f related?

– Inversely (1/T = f)• An object with a frequency of 20 Hertz has

a period of….– 0.05 seconds

Uniform Circular Motion: Observationscentripetal force

• speed stays the same• velocity constantly changing• So there is acceleration that is NOT zero!

definition: UCM refers to the motion of an object in a circle of fixed radius with a constant speed.

Calculating Speed of Circular Motion

t

dv

T

r π2v

d for a circle is the circumference (2 π r) so:

Which bug is moving fastest? Why?

r

3r

• Greater circumference (distance traveled) greater radius greater speed

t

r π2v

r

3r

t

3r π23v

Why is velocity tangent to the circle?

Acceleration

• Towards the center of the circle of motion

• Why towards the center?

2

c

va

r

Acceleration is not zero!

Law of inertia..."... objects in motion tend to stay in motion with the same speed and the same direction unless acted upon by an unbalanced force."

Without a pull towards the center, an object in motion continues along a straight-line path.

With a pull towards the center, an object in motion will be accelerated and change its direction.

Centripetal Force

• An object’s natural path is a straight line (inertia)– Therefore to pull an object out of its natural path a net force

must be present, towards the center of the circle– Acceleration is NOT zero, so F cannot be zero– The force maintains the circle (whether the circle is complete

or partial)

• Where does the force originate?– could be any of typical forces (weight, tension, normal,

applied, or friction) or a combination of those

• Called the Centripetal (center seeking) Force – Fc

What is the equation for centripetal force?

cc maF

r

vac

2

r

mvFc

2

Practice

• A 2.0 kg mass attached to a 1.5 m cord is swung at 8.0 m/s. What is the magnitude of the Fc acting on the mass?

(2)(82)/1.5 = 85 N

CentriFugal Force:

The False Force – it’s only a feeling, not an actual force

Video disk: barrel rideAnti-gravity machine simulation

Examples of Fc

Examples of Fc

Examples of Fc

Examples of Fc

Examples of Fc

video re-cap