Chapter 9 Circular Motion

Did You Know? Did You Know? The tilt of the Earth on its axis and the Earth's revolution cause the seasons NOT the Earth's proximity to the Sun.

Rotations & Revolutions An axis is the straight line around which rotation takes place. Rotation is a spin about an axis located within the body a wheel a satellite Revolution is a spin about an axis outside the body. a wheel rim a satellite orbiting the earth

Rotation and Revolution The Ferris wheel turns about an axis. The Ferris wheel rotates, while the riders revolve about its axis.

Rotations & Revolutions Does a tossed football rotate or revolve? rotates (spins) Does a ball whirled overhead at the end of a string rotate or revolve? revolves about you

Rotation and Revolution Earth undergoes both types of rotational motion. It revolves around the sun once every 365 ¼ days. It rotates around an axis passing through its geographical poles once every 24 hours.

Rotational Speed & Tangential Speed Merry-go-around Rotational speed is same anywhere on the ride (same revolutions/second) Linear speed is tangent to the curved path and different depending on where you ride. Linear speed is perpendicular to the radial direction is called “tangential velocity.” Conceptual Physics: Demo - Rotational Speed - YouTube

Speed Which part of the turntable moves faster—the outer part where the ladybug sits or a part near the orange center? It depends on whether you are talking about linear speed or rotational speed. Linear (tangential) speed depends on rotational speed and the distance from the axis of rotation.

Rotational Speed All parts of the turntable rotate at the same rotational speed. A point farther away from the center travels a longer path in the same time and therefore has a greater tangential speed. A ladybug sitting twice as far from the center moves twice as fast.

Circular Motion…. In symbol form, v ~ r where v is tangential speed and  (pronounced oh MAY guh) is rotational speed. You move faster if the rate of rotation increases (bigger ). You also move faster if you are farther from the axis (bigger r).

Conservation of Angular Momentum DEMO: Conservation of angular momentum - YouTube angular momentum = rotational inertia ´ rotational velocity L = I w Newton's first law for rotating systems: “A body will maintain its state of angular momentum unless acted upon by an unbalanced external torque.”

The linear speed is directly proportional to both rotational speed and radial distance. v = w r What are two ways that you can increase your linear speed on a rotating platform? Answers: Move away from the rotation axis. Have the platform spin faster.

Tangential Speed  

Rotational Speed & Tangential Speed Two coins on turn table, one near center and other near edge. Outer coin has … greater linear speed. Both have same … rotational speed – revolutions per second. Examples: See design on hub cap but not on the tire. Crack-the-whip end person.

Tangential Speed (Linear Velocity) Swinging Meterstick: How fast at any given moment is the 100-cm mark moving compared to the 50-cm mark? The 100-cm mark is twice as far from the center of rotation than the 50-cm mark and has twice the linear speed. Why does a flyswatter have long handle? Long handle amplifies the speed of your hand.

Tapered Wheels of Rail Road Cars Do “Doing Physics” pg. 125 & 126

Rotational Speed A tapered cup rolls in a curve because the wide part of the cup rolls faster than the narrow part.

10.2 Rotational Speed A pair of cups fastened together will stay on the tracks as they roll. The cups will remain on the track. They will center themselves whenever they roll off center.

Rotational Speed When the pair rolls to the left of center, the wider part of the left cup rides on the left track while the narrow part of the right cup rides on the right track. This steers the pair toward the center. If it “overshoots” toward the right, the process repeats, this time toward the left, as the wheels tend to center themselves.

Rotational Speed When a train rounds a curve, the wheels have different linear speeds for the same rotational speed.

Rotational Speed When a train rounds a curve, the wheels have different linear speeds for the same rotational speed.

Centripetal Force Centripetal means “toward the center.” The force directed toward a fixed center that causes an object to follow a circular path is called a centripetal force. Example: If you whirl a tin can on the end of a string, you must keep pulling on the string—exerting a centripetal force. The string transmits the centripetal force, pulling the can from a straight-line path into a circular path

Centripetal Force The force exerted on a whirling can is toward the center. No outward force acts on the can.

Remember…   v = w r

Centripetal Acceleration and Centripetal Force Centripetal Acceleration (ac)- acceleration directed toward the center of the circle change in velocity per unit of time rate at which velocity is changing velocity is changing because the object is constantly changing its direction as it follows a curved path centripetal acceleration = (linear speed)2 ac = v2 symbol:ac radius r unit: m/ s2 if mass is being accelerated toward the center of a circle, it must be acted upon by an unbalance net force that gives it this acceleration Joe is sitting 2m from the center of a merry-go-round that has a frequency of 1. 25 Hz (Hertz is one revolution per second). What is Joe’s centripetal acceleration? What is the direction of the centripetal acceleration?

Centripetal Force  

Centripetal Force Whirling Can at End of a String The string pulls radially inward on the can. By Newton’s Third Law, the can pulls outward on the string – so there is an outward-acting force on the string. This outward force does not act on the can. ONLY inward force on the can.

Spinning Washer The tub wall exerts Fc on the clothes forcing it into a circular path, but not the water. Water escapes bcs no Force acting on it….so water stays in straight line path perpendicular or tangent to the curve.

Centrifugal Force Center-fleeing or Away from Center An apparent outward force on a rotating or revolving body. It is fictitious in the sense that it is not part of an interaction but is due to the tendency of a moving body to move in a straight-line path due to inertia Is useful only in a rotating frame of reference The inward push “feels” like an outward pull to the object in a rotating system (as if a big mass were out there causing gravity) Not a real force – there is no interaction (there is no mass out there pulling on it). There is no action reaction pair of forces

Misconception BIG MISCONCEPTION: centrifugal force pulls outward on an object in a circular path fig 9.7 then string breaks.... misconception.....centrifugal force pulls can from its circular path reality....can goes off in a straight-line path tangent to circle because there is NO FORCE acting on can anymore fig 9.8 only the force from the string acts on the can to pull the can inward there is no outward force acting on the can

Centrifugal “Forces” The only force that is exerted on the whirling can (neglecting gravity) is directed toward the center of circular motion. This is a centripetal force. No outward force acts on the can.

The can provides the centripetal force necessary to hold the ladybug in a circular path.

Centrifugal Force A person in a spinning space habitat feels a force like that of gravity and does pushups just like on earth. Is the force centripetal or centrifugal? How is it different than gravity? Conceptual Physics: Simulated Gravity - YouTube

Centrifugal Forces The can presses against the bug’s feet and provides the centripetal force that holds it in a circular path. The ladybug in turn presses against the floor of the can. Neglecting gravity, the only force exerted on the ladybug is the force of the can on its feet. From our outside stationary frame of reference, we see there is no centrifugal force exerted on the ladybug.

Rotational Inertia An object rotating about an axis tends to remain rotating unless interfered with by some external influence. This influence is called torque. Rotation adds stability to linear motion. Examples: spinning football bicycle tires Frisbee

The greater the distance between the bulk of an object's mass and its axis of rotation, the greater the rotational inertia. Examples: Tightrope walker Metronome

Torque Torque is the product of the force and lever-arm distance, which tends to produce rotation. Torque = force ´ lever arm Examples: wrenches see-saws

Center of Mass The center of mass of an object is the average position of mass. Objects tend to rotate about their center of mass. Examples: Meter stick Rotating Hammer

Stability For stability center of gravity must be over area of support. Examples: Tower of Pisa Touching toes with back to wall Meter stick over the edge Rolling Double-Cone

Direction of Motion Centripetal Force Centrifugal Force

Centripetal Force Centrifugal Force …is applied by some object. Centripetal means "center seeking". Centrifugal Force …results from a natural tendency. Centrifugal means "center fleeing".

What is that force that throws you to the right if you turn to the left in your car? centrifugal force. What is that force that keeps you in your seat when you turn left in your car? centripetal force.

Examples Centripetal Force Centrifugal Force water in bucket moon and earth car on circular path coin on a hanger jogging in a space station Bucket Earth’s gravity Road Friction Hanger Space Station Floor

Example Question Two ladybugs are sitting on a phonograph record that rotates at 33 1/3 RPM. 1. Which ladybug has a great linear speed? A. The one closer to the center. B. The one on the outside edge. C. The both have the same linear speed

Example Question Two ladybugs are sitting on a phonograph record that rotates at 33 1/3 RPM. 1. Which ladybug has a great linear speed? A. The one closer to the center. B. The one on the outside edge. C. The both have the same linear speed

Example Question Two ladybugs are sitting on a phonograph record that rotates at 33 1/3 RPM. 2. Which ladybug has a great rotational speed? A. The one closer to the center. B. The one on the outside edge. C. The both have the same rotational speed

Example Question You sit on a rotating platform halfway between the rotating axis and the outer edge. You have a rotational speed of 20 RPM and a tangential speed of 2 m/s. What will be the linear speed of your friend who sit at the outer edge?

Example Question A. 4m/s B. 2m/s C. 20 RPM D. 40 RPM E. None of these You sit on a rotating platform halfway between the rotating axis and the outer edge. You have a rotational speed of 20 RPM and a tangential speed of 2 m/s. What will be the linear speed of your friend who sit at the outer edge? A. 4m/s B. 2m/s C. 20 RPM D. 40 RPM E. None of these

Example Question A. 4m/s B. 2m/s C. 20 RPM D. 40 RPM E. None of these You sit on a rotating platform halfway between the rotating axis and the outer edge. You have a rotational speed of 20 RPM and a tangential speed of 2 m/s. What will be the rotational speed of your friend who sit at the outer edge? A. 4m/s B. 2m/s C. 20 RPM D. 40 RPM E. None of these

End of Chapter