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**Horizontal Circular Motion**

Show video: Frames of Reference: 17: :45

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**Review If an object travels at a constant velocity a = 0 Fnet = 0**

If an object travels with a changing velocity .

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What if? What if you do not speed up or slow down, but change direction? Velocity changes (vector) Acceleration occurs Fnet At end of slide, show Mechanical Universe 17: :15

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**Centripetal Acceleration**

Centripetal - center seeking points towards the center of the circle sometimes called radial acceleration dependent on v and r

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Example A ball at the end of string is revolving in a horizontal circle of radius 0.6 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

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Example A jet plane traveling at 525 m/sec pulls out of a dive by moving in an arc of radius 6 km. What is the plane’s centripetal acceleration? Change ac to “g” and discuss into g’s.

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**Dynamics of Circular Motion**

If there is an acceleration, Newton’s Second Law requires a net external force Since the acceleration is centripetal, the net force must also be centripetal

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Centripetal Force But that would mean centripetal force is not a real force, but is a net force and caused by something else. Fw, Fn, Ft, Ff

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Okay, that other Force Centrifugal - an outward force acting on an object moving in a circular path Everyone has felt it So, what do you feel? Depends on who “you” are.

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Centrifugal Force If there was a centrifugal force acting on the ball, what would happen if you let it go? Play video: Frames of Reference: 17:45 to end of circular discussion

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Sample Problem A 10 kg mass is attached to a string that has a breaking strength of 200 N. If the mass is whirled in a horizontal circle of radius 0.8 m, what maximum speed can it have?

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**Circular Motion A Review**

In most cases, the string force not only has to provide the force required for circular motion, but also the force required to balance the gravitational force.

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Dynamics Since there is a net force, we need to know which forces are acting ON the object and then solve. A 300 g tetherball is attached to a massless rope 2 m long. If the rope makes an angle of 30o to the vertical, what is the speed of the ball?

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In a version of a “Giant Swing”, the seat is connected to two cables as shown. The seat swings in a horizontal circle at a rate of 32 rpm. If the seat weighs 255 N and a 825 N person is sitting in it, find the tension in each cable. Sample Problem

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**Circular Motion and Friction**

This required force is provided by the friction force between the tires and the road. But remember ….. The friction force has a maximum value, and there is a maximum speed with which you can make the turn.

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Highway Curves A 1000 kg car rounds a curve on a flat road of radius 50 m at a speed of 15 m/sec. What minimum coefficient of friction is needed for the car to safely navigate the corner?

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Sample A flat puck of mass M is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block of mass m. What is the speed of the flat puck if the radius of the circle is R?

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sample A 4 kg object is attached to a vertical rod by two strings. The object rotates in a horizontal circle at constant speed 6 m/sec. Find the tension in each of the strings.

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Vertical Circles

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Vertical Circles Motion in a vertical circle is no different, other than the weight of the object now comes into play. Look at the forces acting on the passenger to keep them in the circular path both at the top and the bottom.

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Ferris Wheel A passenger on a Ferris wheel moves in circle of radius 8 m. The passenger’s mass is 60 kg and the wheel completes one revolution in 10 sec at a constant speed. What is the normal force of the seat on the passenger both at the top and the bottom?

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Example A bowling ball weighing 70 N is attached to a ceiling by a 4 m long rope. The ball is pulled back until the rope makes an angle of 30o to the vertical. The ball is then released. Determine: the speed of the ball when the rope is vertical. the tension in the rope when the rope is vertical.

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**amusement Park Physics**

What is the minimum speed that a roller coaster must be traveling when upside down at the top of a circle so that the passengers do not fall out? Assume a radius of 7.4 m.

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**amusement Park Physics**

If the riders are at the top with the speed you just found, how fast will they be moving when they get to the bottom? What will the normal force be on the passengers at the bottom assuming they are still moving in a circular path?

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**Amusement park physics**

A roller-coaster car has a mass of 500 kg when fully loaded with passengers. what is the maximum speed the vehicle can have at B and still remain on the track? with that speed at b, what is the normal force of the track on the car at point A?

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