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Rotational Equilibrium 4/21 & 4/22 Do Now – TAKE ONE Don’t forget your HW for tonight!!! Read & Study 10.1, 10.4, 10.6 Complete #1-3, 8-10, 18-20 (p. 147) 10 points!!!

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Rotational Equilibrium The center of mass of an object is the point located at the object’s average position of mass. (CM) The center of gravity of an object is the point located at the object’s average position of weight. (CG) **For this course, we can use the terms Center of Gravity [CG] and Center of Mass [CM] interchangeably in most scenarios** Center of Mass

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Rotational Equilibrium Location of the Center of Mass For a symmetrical object, such as a baseball, the center of mass is at the geometric center of the object. For an irregularly shaped object, such as a baseball bat, the center of mass is toward the heavier end. Center of Mass

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Rotational Equilibrium The center of mass for each object is shown by the red dot. 11.3 Center of Mass

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Rotational Equilibrium The centers of mass of the baseball and of the spinning baseball bat each follow parabolic paths… All objects thrown in the air will rotate about their CG in this way Center of Mass

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Rotational Equilibrium As an object slides across a surface, its center of mass follows a straight-line path. If the wrench were tossed into the air, its center of mass would follow a smooth parabola. Center of Mass

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Rotational Equilibrium Objects not made of the same material throughout may have the center of mass quite far from the geometric center. Consider a hollow ball half filled with lead. The center of mass would be located somewhere within the lead part. The ball will always roll to a stop with its center of mass as low as possible. Center of Mass http://www.youtube.com/watch? v=dFzhjnjXc2o

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Rotational Equilibrium Locating the Center of Gravity The center of gravity (CG) of a uniform object is at the midpoint, its geometric center. The CG is the balance point. Supporting that single point supports the whole object. Center of Gravity

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Rotational Equilibrium The weight of the entire stick behaves as if it were concentrated at its center. The small vectors represent the force of gravity along the meter stick, which combine into a resultant force that acts at the CG. Center of Gravity

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Rotational Equilibrium The weight of the entire stick behaves as if it were concentrated at its center. The small vectors represent the force of gravity along the meter stick, which combine into a resultant force that acts at the CG. Center of Gravity

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Rotational Equilibrium The CG of an object may be located where no actual material exists. The CG of a ring lies at the geometric center where no matter exists. The same holds true for a hollow sphere such as a basketball. Center of Gravity

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Rotational Equilibrium The center of gravity of a person is not located in a fixed place, but depends on body orientation. Center of Gravity of People

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Rotational Equilibrium When you stand straight up with your arms hanging at your sides, your CG is within your body, typically 2 to 3 cm below your navel, and midway between your front and back. Raise your arms vertically overhead. Your CG rises 5 to 8 cm. Bend your body into a U or C shape and your CG may be located outside your body altogether. Center of Gravity of People

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Rotational Equilibrium A high jumper executes a “Fosbury flop” to clear the bar while his CG nearly passes beneath the bar. Center of Gravity of People

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Rotational Equilibrium think! Can an object have more than one CG? Center of Gravity

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Rotational Equilibrium think! Can an object have more than one CG? Answer: Yes & No No more than one CG at a time…BUT the location of an object’s CG can change! A rigid object has one CG. If a non rigid object, such as a piece of clay or putty (or a person!) is distorted into different shapes, then its CG may change as its shape is changed. Even then, it has one CG for any given shape. Center of Gravity

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Rotational Equilibrium If the center of gravity of an object is DIRECTLY ABOVE the area of support, the object will remain upright. THE RULE FOR TOPPLING (back of your paper)

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Rotational Equilibrium The block topples when the CG extends beyond its support base. THE RULE FOR TOPPLING

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Rotational Equilibrium The Leaning Tower of Pisa does not topple over because its CG lies above its base. THE RULE FOR TOPPLING

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Rotational Equilibrium The support base of an object does not have to be solid. An object will remain upright if the CG is VERTICALLY above its base of support. The shaded area bounded by the bottom of the chair legs defines the support base of the chair. When you stand, your CG is somewhere above the area bounded by your feet. AREA OF SUPPORT

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Rotational Equilibrium When you stand, your CG is somewhere above your support base, the area bounded by your feet. In unstable situations, as in standing in the aisle of a bumpy- riding bus, you place your feet farther apart to increase this area. Standing on one foot greatly decreases this area. Center of Gravity of People

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Rotational Equilibrium Video Questions (PBS VIDEO – Center of Gravity ) http://www.pbs.org/opb/circus/classroom/circus-physics/center-mass/ #1-4 http://www.pbs.org/opb/circus/classroom/circus-physics/center-mass/

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Rotational Equilibrium A DAY - Today’s Goals Finish #1-4 Complete #5-6 as a class Complete #7-9 in groups of your choosing Check in at stop sign Finish all of the activities in your POGIL, leaving 7 minutes before the bell.

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Rotational Equilibrium B DAY - Today’s Goals Finish #1-4

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Rotational Equilibrium B DAY - Today’s Goals Finish #1-4 Complete #5-6 as a class

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Rotational Equilibrium B DAY - Today’s Goals Finish #1-4 Complete #5-6 as a class Complete 7 - 9

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Rotational Equilibrium 7. We don’t know exactly WHERE it is…just that it is ABOVE the area of support!

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Rotational Equilibrium 8. IN other words… Its CG is NOT above its area of support!

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Rotational Equilibrium 9. IN other words… Its CG is above its area of support!

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Rotational Equilibrium Station 2: CHAIR LIFT 1.Let’s have a contest, boys vs. girls! Challenge a member of the opposite sex to compete in this activity with you. Stand EXACTLY 2 foot lengths away from a wall. Place a chair between yourself and the wall Bend over with a straight back (so that your back is perfectly parallel with the floor, and perpendicular to the wall), and let your head lean against the wall KEEP YOUR HEAD AGAINST THE WALL and lift the chair off the floor. Then, attempt to straighten up. 2. FIVE minutes to complete the station and #16 ***HINT – READ P. 145!!!!

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Rotational Equilibrium Station 2: CHAIR LIFT Who has a LOWER CG? A.Girls B.Boys C.Same

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Rotational Equilibrium Station 3: Wall Stand Stand with the back of your feet directly against a wall. Do not bend your knees, and try to touch your toes. 1. FOUR minutes to complete the station and the questions!!

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Rotational Equilibrium You can lean over and touch your toes without toppling only if your CG is above the area bounded by your feet. Center of Gravity of People

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Rotational Equilibrium

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Station 5: Tippy Toes Stand facing a wall with your toes against the wall. Place your nose against the wall and stand on your tip toes. 1. FOUR minutes to complete the station and the questions!

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Rotational Equilibrium

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GO BACK & FINISH… Station 1: Sit on a chair Station 4: Meter Stick CHECK IN AT STOP SIGNS!!!

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Rotational Equilibrium EXIT SLIP Complete and turn in Don’t forget your HW for tonight!!! Read & Study 10.1, 10.4, 10.6 Complete #1-3, 8-10, 18-20 (p. 147)

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