2. Objective Describe and calculate centripetal forces and accelerations.2

3. Centripetal Force
Why does a roller coaster stay on a track upside down on a loop? 3

4. Centripetal Force
We usually think of acceleration as a change in speed.
Because velocity includes both speed and direction, acceleration can also be a change in the direction of motion.

5. Centripetal Force
Any force that causes an object to move in a circle is called a centripetal force.
A centripetal force is always perpendicular to an object’s motion, toward the center of the circle.

6. Calculating centripetal force
The magnitude of the centripetal force needed to move an object in a circle depends on the object’s mass and speed, and on the radius of the circle.

7. Fc = mv2 r Centripetal Force Mass (kg) Linear speed (m/sec)
force (N)
Fc = mv2 r
Radius of path
(m)

8. Calculating centripetal force
A 50-kilogram passenger on an amusement park ride stands with his back against the wall of a cylindrical room with radius of 3 m. What is the centripetal force of the wall pressing into his back when the room spins and he is moving at 6 m/sec?
You are asked to find the centripetal force.
You are given the radius, mass, and linear speed.
Use: Fc = mv2 ÷ r
Solve: Fc = (50 kg)(6 m/s)2 ÷ (3 m) = 600 N

9. Centripetal Acceleration
Acceleration is the rate at which an object’s velocity changes as the result of a force.
Centripetal acceleration is the acceleration of an object moving in a circle due to the centripetal force.

10. Centripetal Acceleration
Speed
(m/sec)
Centripetal
acceleration (m/sec2)
ac = v2 r
Radius of path
(m)

12. Calculating centripetal acceleration
A motorcycle drives around a bend with a 50-meter radius at 10 m/sec. Find the motor cycle’s centripetal acceleration and compare it with g, the acceleration of gravity.
You are asked for centripetal acceleration and a comparison with g (9.8 m/s2).
You are given the linear speed and radius of the motion.
Use: ac = v2 ÷ r
4. Solve: ac = (10 m/s)2 ÷ (50 m) = 2 m/s2
The centripetal acceleration is about 20%, or 1/5 that of gravity.

13. Centrifugal Force
We call an object’s tendency to resist a change in its motion its inertia.
An object moving in a circle is constantly changing its direction of motion.
Although the centripetal force pushes you toward the center of the circular path...it seems as if there also is a force pushing you to the outside.
This “apparent” outward force is often incorrectly identified as centrifugal force.

14. Centrifugal Force
Centrifugal force is not a true force exerted on your body.
It is simply your tendency to move in a straight line due to inertia.
This is easy to observe by twirling a small object at the end of a string.
When the string is released, the object flies off in a straight line tangent to the circle.

15. v = 2π v = ω r t
ω = θ θ = s
t r
Fc = mv² Fc = m ac r

16. Centripetal Acceleration
ac = v² r
ac = (rω)² ac = r ω²