Centripetal Force
Fc = mv²/r — the net force that keeps an object moving in a circle
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.
Go Nittany Lions!! 
Identify the Fc and v. What is the relationship between Fc and v?
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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
AP Physics, p. 130 — problems 8, 11
Ex: Finding the Radius
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.
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
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Direct Relationship
(Both variables on top)
| Mass | Fc |
|---|---|
| x 2 | x 2 |
| x 3 | x 3 |
| x 4 | x 4 |
| x 1/2 | x 1/2 |
| x 1/4 | x 1/4 |
2. Fc & Radius?
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Inverse Relationship
(One variable on top, other on bottom)
| Fc | r |
|---|---|
| x 1/2 | x 2 |
| x 1/3 | x 3 |
| x 1/4 | x 4 |
| x 2 | x 1/2 |
| x 4 | x 1/4 |
3. Fc & Velocity?
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| V | Fc |
|---|---|
| x 2 | x 4 |
| x 3 | x 9 |
| x 4 | x 16 |
| x 1/2 | x 1/4 |
| x 1/4 | x 1/16 |
2 Step Challenge
A toy car moves in a circular track of radius 5.00 m in 10.0 seconds.
Find: the car's centripetal acceleration.
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Hammer Throw
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/
NYSSLS Reading Passage · Circular Motion
Eyes You'll Never See: The Many Uses of Artificial Satellites
Open Reading Passage → Regents Practice Version →Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A 5.0 kg object moves in a circle at 10. m/s with a centripetal force of 1000. N. What is the radius?
2. The mass of an object moving in a circle is doubled while speed and radius stay the same. The centripetal force
3. The speed of an object moving in a circle triples while mass and radius stay the same. The centripetal force becomes
4. A toy car goes once around a circular track of radius 5.00 m in 10.0 s. What is its speed?
5. Which statement about centripetal force is correct?
Designing a Highway Curve
A 1200-kg car travels around a flat (unbanked) curve of radius 50. m at a constant speed of 20. m/s.
What is the magnitude of the centripetal force on the car?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. On a flat road, what supplies this centripetal force?
C2. Substitute numerical values into a mathematical representation that can be used to determine the centripetal acceleration of the car. Then calculate the acceleration.
C3. A traffic engineer makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using mathematical relationships.
C4. The maximum static friction force between the tires and the dry road is 12,000 N. Determine the maximum speed at which the car can round the 50.-m curve without skidding.
C5. The road suddenly becomes icy and friction drops to nearly zero. Which path does the car follow (top view)?
C6. Highway engineers decide to bank (tilt) this curve. Explain how banking helps cars turn safely, and identify one drawback or constraint of a banked curve.
