1. Uniform Circular Motion

2. What is a circle?
In geometry: the set of all points in a plane that are at a given distance from a given point.

3. What is a circle?
In physics: All points whose position vector has the same beginning and the same length

4. Radial Position Vectors

5. Uniform Circular Motion
Constant speed
But not constant velocity
The velocity is always changing direction

6. Velocity vector is perpendicular to position vector. It’s a tangent.
Uniform Circular Motion
Velocity vector is perpendicular to position vector. It’s a tangent. v p
What happened when you let go of string during lab?

7. Uniform Circular Motion
Period - the time it takes to go around the circle once
Symbol - T

8. Uniform Circular Motionv
Acceleration vector is perpendicular to velocity vector and pointed to center of circle. ac
centripetal acceleration (ac)
“center seeking”

9. Uniform Circular Motion
Use geometry’s similar triangles: ac = v2/r ac = centripetal acceleration (m/s2) v = velocity (m/s) r = radius of circle (m)

10. centripetal force Fc = mac= mv2/r
Uniform Circular Motion
centripetal force Fc = mac= mv2/r
Fc = centripetal force (N) m = mass of object (kg) ac = centripetal acceleration (m/s2)

11. centripetal force Fc = mac
Uniform Circular Motion v
centripetal force Fc = mac Fc

12. Example
A 1.6 kg object travelling in a circle has a centripetal acceleration of 9.0 m/s2. What is the centripetal force acting on the object?
Given
Unknown
Equation
Substitute
Solve

13. A 500 kg race car rounds a curve of 10 m with a speed of 35 m/s
A 500 kg race car rounds a curve of 10 m with a speed of 35 m/s. What is the magnitude of the centripetal force acting on the car?
Given
Unknown
Equation
Substitute
Solve

14. Demestrius is riding a roller coaster at Six Flags and feels a centripetal force of 1700 N when going around a sharp curve. If his mass is 80 kg, what is his centripetal acceleration?
Given
Unknown
Equation
Substitute
Solve

15. Dillen, with a weight of 580 N, has a centripetal acceleration of 3 m/s2 as he rounds a bend in a cross country match. What is the magnitude of the centripetal force acting on Dillen?
Given
Unknown
Equation
Substitute
Solve

16. Work Your Turn Problems