1. Aim: How do we explain centripetal motion?

2. Uniform Circular Motion
An object that moves in a circle at constant speed is said to undergo uniform circular motion (centripetal motion).

3. Uniform Circular Motion-turn and talk
How do we know that the object (blue particle) is accelerating? Its velocity changes because it changes direction
What is the direction of the object’s acceleration? To the center of the circle
What is the direction of the object’s instantaneous velocity? Tangent to the circular path

4. Uniform Circular Motion
The centripetal acceleration of an object is always directed toward the center. The instantaneous velocity of an object in centripetal motion is always directed tangent to the circular path.

5. The Centripetal force
The centripetal force has the same direction as the centripetal acceleration. The centripetal force is not a distinct type of force. It is a net force, and is thus always the result of other forces.

6. Sample Question
Draw a vector representing the direction of the object’s acceleration at point A. (The vector direction down) Draw a vector representing the direction of the object’s instantaneous velocity at point A. (The vector directed to the left)

7. Regents checkpoint # 1
The 2 kg mass moves in a circle at a constant speed of 4 m/s and is tied to the end of a string that is 0.5 mg long.
What is the direction of the acceleration of the mass in the position shown?
a) A b) B c) C d) D

8. REGENTS CHECKPOINT # 2
The 2 kg mass moves in a circle at a constant speed of 4 m/s and is tied to the end of a string that is 0.5 mg long. If the string is cut when the mass is at the position shown, what direction will the mass initially move? a) Up b) Down c) Left d) Right

9. Regents Checkpoint # 3
What is the direction of the centripetal force acting on the 5 kg mass at the position shown? a) A b) B c) C d) D
A 5 kg mass moves in a circle counterclockwise at a constant speed of 20 m/s. The radius of the circle is 20 m.

10. Regents Checkpoint # 4
A 5 kg mass moves in a circle counterclockwise at a constant speed of 20 m/s. The radius of the circle is 20 m.
What is the direction of the instantaneous velocity of the object at the position shown?
a) Towards A b) Towards B c) Towards C d) Towards D

11. Equation for Centripetal Acceleration
Centripetal Acceleration = ac Speed = v Radius of circular path = r ac = v2/r

12. Equation for centripetal force
Fc=mac Fc = centripetal force m= mass ac = centripetal acceleration

13. Problem 1
The 2 kg rock moves clockwise in a circle at a constant speed of 4 m/s and is tied to the end of a string that is 0.5 m long.
ac=v2/r=(4 m/s)2/(0.5m)
ac=32 m/s2
Fc =mac
Fc =2kg(32m/s2)=64 N
Calculate the centripetal acceleration of the rock.
Calculate the centripetal force acting on the rock.

14. Problem 2
A 5 kg mass moves in a circle counterclockwise at a constant speed of 20 m/s. The radius of the circle is 20 m.
Calculate the acceleration of the mass.
Calculate the centripetal force acting on the mass.
ac=v2/r=(20m/s)2/20m=20m/s2
Fc =mac =(5kg)(20m/s2)=100N

15. Thought question-turn and talk
Assume you drive around a sharp turn with a small radius at a speed of 10 m/s. Later in the day you drive around a more gradual turn with a larger radius at the same speed of 10 m/s. In which situation was your centripetal acceleration larger? The acceleration is larger around the sharp turn. In which situation was the centripetal force acting on you greater? The centripetal force is larger around the sharp turn.

16. THOUGHT QUESTION-TURN AND TALK
Assume you drive around a turn of a given radius r = 10 m with a slow speed. Later in the day you drive around a turn of the same radius of 10 m at a significantly faster speed. In which situation was your centripetal acceleration larger? The centripetal acceleration is larger at the faster speed. In which situation was the centripetal force acting on you greater? The centripetal force is greater at the faster speed.

17. Reading passage
Any object moving in a circle (or along a circular path) experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle. This is the centripetal force requirement. The word centripetal is merely an adjective used to describe the direction of the force. We are not introducing a new type of force but rather describing the direction of the net force acting upon the object that moves in the circle. Whatever the object, if it moves in a circle, there is some force acting upon it to cause it to deviate from its straight-line path, accelerate inwards and move along a circular path. Three such examples of centripetal force are shown below. As a car makes a turn, the force of friction acting upon the turned wheels of the car provides centripetal force required for circular motion. As a bucket of water is tied to a string and spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion. As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.

18. Centripetal vs centrifugal
Centripetal force is the overall force acting on an object to sustain its circular motion Centrifugal force is the apparent force pushing outwards on an object undergoing centripetal motion. It is called a fictitious force.

19. Artificial gravity
A spaceship can produce a feeling of gravity by accelerating in a circle. What would the centripetal acceleration of a spaceship have to be to create the feeling of being on Earth?