Chapter 6: Circular Motion• Summary• Motion in a vertical circle• Apparent Weight

Extending beyond Physics 151• Rotational analog to translational motion

• Moment of Inertia• Angular Momentum

• Center of Mass

Week 16 Day 3 - Last day of Class

Slide 15-37

Announcements• Exam 3 grades will post and exams will be in boxes by noon

tomorrow – An email will be sent out • Last Worksheet may be turned in Monday by 5 PM w/o late

penalty. Solution will post by 6 PM

• Exam 2 make-up exam will start at 1:30 PM on Tuesday, 12/14 in RH 115.

• You will have a few minutes to look the exam over. • Once you start writing, you will get the average of the two

exam scores

• Final Exam will be next Wednesday from 7:00 - 9:45 AM• Final Exam notes for this semester will post tomorrow

- last year’s final exam notes are already posted• Exam Prep Session will be Monday from 2 – 4 PM

in RH 114/116

Week 16 Day 3 - Last day of Class

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When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because

A. the speed is changing.B. the direction is changing.C. the speed and the direction are changing.D. the ball is not accelerating.

Checking Understanding

Slide 6-13

AnswerWhen a ball on the end of a string is swung in a vertical circle, the ball is accelerating because

A. the speed is changing.B. the direction is changing.C. the speed and the direction are changing.D. the ball is not accelerating.

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When a ball on the end of a string is swung in a vertical circle:What is the direction of the acceleration of the ball?

A. Tangent to the circle, in the direction of the ball’s motion

B. Toward the center of the circle

Checking Understanding

Slide 6-15

AnswerWhen a ball on the end of a string is swung in a vertical circle:What is the direction of the acceleration of the ball?

A. Tangent to the circle, in the direction of the ball’s motion

B. Toward the center of the circle

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For the ball on the end of a string moving in a vertical circle:What is the direction of the net force on the ball?

A. tangent to the circleB. toward the center of the circleC. there is no net force

Checking Understanding:Circular Motion Dynamics

Slide 6-19

Answer

For the ball on the end of a string moving in a vertical circle:What is the direction of the net force on the ball?

A. tangent to the circleB. toward the center of the circleC. there is no net force

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For the ball on the end of a string moving in a vertical circle:What force is producing the centripetal acceleration of the ball?

A. gravityB. air resistanceC. normal forceD. tension in the string

Checking Understanding:Circular Motion Dynamics

Slide 6-17

Answer

For the ball on the end of a string moving in a vertical circle:What force is producing the centripetal acceleration of the ball?

A. gravityB. air resistanceC. normal forceD. tension in the string

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Loop the LoopConsider a ball on a string making a vertical circle.

• Draw a free-body diagram of the ball at the top and bottom of the circle

• Rank the forces in the two diagrams. Be sure to explain the reasoning behind your rankings

• Find the minimum speed of the ball at the top of the circle so that it keeps moving along the circular path • What would happen if the speed was less than the

minimum?• What would happen if the speed was more than

the miniumum?

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Keep the Water in the Bucket

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A roller-coaster car has a mass of 500 kg when fully loaded with passengers as shown on the right.

1. If the car has a speed of 20.0 m/s at point A, what is the force exerted by the track at this point?What is the apparent weight of the person?

2. What is the maximum speed the car can have at point B and stay on the track?

Roller Coaster and Circular Motion

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We have mainly discussed particle motion• This describes motion of the center of mass• What about rotational motion about the center of mass

• Every motion quantity we have looked at in kinematics, Forces, momentum, and Energy has an analogous quantity in Rotation.

• Every equation has an analog too• Rotational equations look exactly the same

• Examples• Position => theta• Force => torque• Kinetic Energy => Rotational Kinetic Energy• Momentum => Angular momentum• Mass => Moment of Inertia

Every quantity we studied has a rotational analog

Slide 15-37

Additional Example ProblemsAt Talladega, a NASCAR track, the turns have a 370 m radius and are banked at 33°. At what speed can a car go around this corner with no assistance from friction?

The Globe of Death is a spherical cage in which motorcyclists ride in circular paths at high speeds. One outfit claims that riders achieve a speed of 60 mphin a 16 ft diameter sphere. What would be the period for this motion? What would be the apparent weight of a 60 kg rider at the bottom of the sphere?Given these two pieces of information, does this high speed in this small sphere seem possible?

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