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Chapter Chapter 8 8 Rotational Rotational Motion Motion
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### Transcript of Chapter 8 Rotational Motion Forces and circular motion Circular motion = accelerated motion...

• Chapter 8Rotational Motion

• Forces and circular motionCircular motion = accelerated motion (direction changing)Centripetal acceleration presentCentripetal force must be actingCentrifugal force - apparent outward tug as direction changesCentripetal force ends: motion = straight line

• Direction ofMotionCentrifugal ForceCentripetalForce

• Centripetal Forcehas different origin (friction, tension, gravity, etc.).Centripetal means "center seeking".Centrifugal Force(not a real force)results from a natural tendencyto keep a state of motion (inertia).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.

• Exampleswater in bucket

moon and earth

car on circular path

coin on a hanger

jogging in a space stationCentripetal ForceBucket

Earths gravity

Hanger

Space Station FloorCentrifugal ForceInertia

Inertia

Inertia

Inertia

Inertia

• Circular MotionLinear speed - the distance moved per unit time. Also called simply speed.

Rotational speed - the number of rotations or revolutions per unit time.

Rotational speed is often measured in revolutions per minute (RPM).

• Angular Position, Velocity, and Acceleration

• Angular Position, Velocity, and AccelerationDegrees and revolutions:

• Angular Position, Velocity, and AccelerationArc length s, measured in radians:

• Connections Between Linear and Rotational Quantities

• Connections Between Linear and Rotational Quantities

• 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.

• Connections Between Linear and Rotational Quantities

• Connections Between Linear and Rotational QuantitiesThis merry-go-round has both tangential and centripetal acceleration.

• Center of MassThe center of mass of an object is the average position of mass.

Objects tend to rotate about their center of mass.

Examples: Meter stickMap of TexasRotating Hammer

• Center of Mass and BalanceIf an extended object is to be balanced, it must be supported through its center of mass.

• Center of Mass and BalanceThis fact can be used to find the center of mass of an object suspend it from different axes and trace a vertical line. The center of mass is where the lines meet.

• 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 footballbicycle tiresFrisbee

• The greater the distance between the bulk of an object's mass and its axis of rotation, the greater the rotational inertia.

Examples: Tightrope walkerInertia BarsRing and Disk on an InclineMetronome

• TorqueFrom experience, we know that the same force will be much more effective at rotating an object such as a nut or a door if our hand is not too close to the axis.This is why we have long-handled wrenches, and why doorknobs are not next to hinges.

• TorqueTorque is the product of the force and lever-arm distance, which tends to produce rotation.

Torque = force lever armExamples: wrenchessee-saws

• We define a quantity called torque:The torque increases as the force increases, and also as the distance increases.

• Only the tangential component of force causes a torque:

• StabilityFor stability center of gravity must be over area of support.

Examples: Tower of PisaTouching toes with back to wallMeter stick over the edgeRolling Double-Cone

• Conservation of Angular Momentumangular momentum = rotational inertia rotational velocityL = 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.

• Conservation of Angular MomentumIf the net external torque on a system is zero, the angular momentum is conserved.The most interesting consequences occur in systems that are able to change shape:

• Examples: 1. ice skater spin2. cat dropped on back3. Diving into water4. Collapsing Stars (neutron stars)

• Example QuestionTwo 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 QuestionTwo 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 QuestionTwo 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 QuestionYou 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 QuestionYou 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/sB. 2m/sC. 20 RPMD. 40 RPME. None of these