Do Now warm-up prompt

Centripetal Force (Fc) — the force directed toward the center of a circle that keeps an object moving in a uniform circular path

Fc and r Relationship

a is greatest from A to B. r is small.

A car moving in a circle is always turning in the same direction.

Penn State Schuylkill

Go Nittany Lions!! Nittany Lion mascot

Identify the Fc and v. What is the relationship between Fc and v?

[ Flash ]

Cut the Rope

LINK — Author: Barb Newitt

D. Centripetal Force

(Fc) — force directed toward center of circle which keeps an object moving in a uniform circular path

Fc = mac = mv²/r

AP Physics, p. 130 — problems 8, 11

Basketball spinning on a fingertip

Ex: Finding the Radius

Given

A 5.0 kg object moves in a circle at a constant speed of 10. m/s.
Find: the radius of the object's circular path if the object's centripetal force is 1000. N.

Fc = mv²/r → 1000. N = (5.0 kg)(10. m/s)²/r

1000. = 500/r → 1000r = 500

r = .50 meters

Uniform circular motion problem diagram
Image created by John Wetzel, founding author of WikiPremed. Released under a Creative Commons Attribution 3.0 License. — WikiPremed Kinematics Image Archive

Great Centripetal Force Demo

Show Me The Physics YouTube Channel

E. Changing Centripetal Force

How Fc responds to changes in mass, radius, and velocity

1. Fc and Mass?

Put your mouse over each variable above

[ Flash ]

Direct Relationship
(Both variables on top)

MassFc
x 2x 2
x 3x 3
x 4x 4
x 1/2x 1/2
x 1/4x 1/4

2. Fc & Radius?

[ Flash ]

Inverse Relationship
(One variable on top, other on bottom)

Fcr
x 1/2x 2
x 1/3x 3
x 1/4x 4
x 2x 1/2
x 4x 1/4

3. Fc & Velocity?

[ Flash ]

Direct Square Relationship

(Both variables on top, one is squared)

Panda swinging nunchucks in a circle
VFc
x 2x 4
x 3x 9
x 4x 16
x 1/2x 1/4
x 1/4x 1/16

2 Step Challenge

Given

A toy car moves in a circular track of radius 5.00 m in 10.0 seconds.
Find: the car's centripetal acceleration.

ac = V²/r    r = 5.00 m, t = 10.0 sec, a = ?

Need to first find V!

V = Δd/Δt = (2πr)/t

Scientist teaching geometry

V = [2π(5.00 m)] / (10.0 sec)

V = 3.14 m/s

ac = V²/r = (3.14 m/s)² / (5.00 m)

ac = 1.97 m/s²

[ Flash ]

Hammer Throw

Timbo riding a merry-go-round

Teaching from Space: Centripetal Force

This media asset is adapted from video provided by NASA's Teaching From Space program.
Produced by WNET.org
http://www.teachersdomain.org/resource/npe11.sci.phys.maf.centripetal/