Circular Motion Ch. 10 in your text book Objectives Students will be able to: 1) Define rotation and revolution 2) Calculate the rotational speed of an object 3) Calculate the centripetal acceleration of an object 4) Calculate the centripetal force of an object
Rotate vs. Revolve What is the difference between rotating and revolving? Rotate spins about internal axis Revolve moves around external axis With your partner, see if you can find and example of something that both rotates and revolves.
Rotational Speed Thus far, we ve only discussed linear speed/velocity. When you rotate, you have both a linear speed and a rotational speed. Think of a merry-go-round. Where do you stand if you want to move the fastest?
Rotational Speed Which dot on the merry-go-round completes a circle first? They both complete a circle in the same amount of time
Rotational Speed Rotational speed is often measured in rotations per minute, or RPM. It tells you how many times you completed a circle in a certain time period.
Linear Speed How far did each dot travel in one revolution? C = 2πr The green dot is farther from the axis so it travels a longer distance than the blue dot, but in the same amount of time
Linear Speed Linear speed is measured in m/s. It is how far you went (the circumference) over a period of time Distance for one revolution v = 2πr t Time for one revolution
Rotational Speed Example: A record player spins at 33 RPM. How long does it take to make one revolution? 33 rev 1 min 60 s 33rev or 60 s 33 rev = 1.82 s/rot
Rotational Speed Example: If there were a lady bug sitting at the edge of the 30 cm record from the last slide, what would its linear speed be? v = 2πr t v = 2π(.15) 1.82 v =.52 m/s
Rotational Speed Example: A merry-go-round is rotating at 25 RPM. What is the linear speed of a person sitting 2 m from the center? 60 s 25 rot = 2.4 s/rot v = 2πr t v = 2π(2) 2.4 v = 5.24 m/s
Rotational Speed If something flies off the merry-go-round, what direction will it go? Notice that the arrow is tangent to the circle. Linear speed is also referred to at tangential speed. The arrow points in the direction of the velocity.
Rotational Speed What do you notice happens to the direction of the velocity as the dot moves around the circle? The speed is constant, but the direction is changing Change in velocity = acceleration
Rotational Speed Acceleration is a change in velocity. This acceleration is called centripetal acceleration. Centripetal means center seeking. For something that is rotating, the acceleration vector will always point to the axis of rotation
Centripetal Acceleration a c = v2 r a c is the centripetal acceleration v is the linear speed r is the radius (distance from the axis of rotation) The unit for centripetal acceleration is m/s 2
Centripetal Acceleration Example: If there were a lady bug sitting at the edge of the 30 cm record, what would its centripetal acceleration be? A few slides ago, we found the linear a c = v2 r speed to be.52 m/s a c =.522.15 a c = 1.79 m/s 2
Centripetal Acceleration Example: A merry-go-round is rotating at 25 RPM. What is the centripetal acceleration of a person sitting 2 m from the center? a c = v2 r a c = 5.242 2 a c = 13.73 m/s 2 What does Newton s 2 nd Law tell us?
Centripetal Force When there is centripetal acceleration, there is centripetal force. The equation follows the same pattern as we had for linear motion: F net = ma F c = ma c = mv2 r This is not a force like tension or weight. It is not drawn on a free body diagram. It is the net force for when things are going in a circle. You only use it when there is a force that causes an object to move in a circle.
Centripetal Force Centripetal force is the net force when there is a force that causes an object to move in a circle. How do you know what force causes it to move in a circle? When you remove that force, the object will move in a straight line, not in a circle.
Centripetal Force Example: A tennis ball is attached to a string. The ball is being swung in a circle horizontally. Which force is causing the ball to move in a circle? Draw a free body diagram to help you. F T F w Centripetal means center seeking. Which force is pointed toward the middle of the circle that the ball is making?
Centripetal Force Example: If there were a 20 g lady bug sitting at the edge of the 30 cm record, what force is causing it to move in a circular motion?
Centripetal Force Example: When a roller coaster does a loop, which force causes it to move in a circle?
Centripetal Force Example: Which force causes circular motion for the figure skater in the picture below?
Centripetal Force What force causes the Earth to rotate around the sun?
Centripetal Force Example: If there were a 20 g lady bug sitting at the edge of the 30 cm record, what would be the centripetal force that it feels? A few slides ago, we found the centripetal acceleration to be 1.79 m/s 2 a c = 1.79 m/s 2 m = 20 g =.02 kg F c = ma c F c = (.02)(1.79) F c =.036 N
Centripetal Force Example: A merry-go-round is rotating at 25 RPM. What is the centripetal force felt by a 40 kg person sitting 2 m from the center? A few slides ago, we found the centripetal acceleration to be 13.73 m/s 2 a c = 13.73m/s 2 m = 40 kg F c = ma c F c = (40)(13.73) F c = 549.2 N
Centripetal Force This is not a force like tension or weight. It is not drawn on a free body diagram. It is the net force for when things are going in a circle. You only account for it when there is a force that causes an object to move in a circle.
To finish up On a piece of paper, please 1) Explain how area affects pressure and force. 2) Calculate pressure created by a 50 kg person standing on a 1 m diameter circle.
Rotational Activity 1) Tie a string to a rubber stopper, thread it through a pen case, and tie the other end to a mass (> 100g) 2) Spin the stopper to lift the mass. See if you can get the mass to stay put at one height. 3) What do you notice about how fast you spin the stopper and how much effort it takes to hold the mass at a given height? 4) Change the mass and see how it affects how fast you have to spin the stopper. 5) Add more mass to the stopper and see how it affects how much effort it takes to lift the mass.