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Physics Fundamentals: Circular Motion & Work-Energy Theorems

Understand centripetal acceleration, gravitational force, work, kinetic energy, center of mass, angular momentum in physics with practical examples and detailed explanations.

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Physics Fundamentals: Circular Motion & Work-Energy Theorems

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  1. Help Session November 12th MAP 306 5-7 PM SPECIAL OFFICE HOURS: Tuesday: 11AM-1PM

  2. Uniform circular motion is due to a centripetal acceleration This acceleration is alwayspointing to the center This acceleration is due to a net force arad = v2/R

  3. A diagram of gravitational force

  4. We want to place a satellite into circular orbit 300km above the earth surface. What speed, period and radial acceleration it must have?

  5. What is “work” as defined in Physics? • Formally, work is the product of a constant force F through a parallel displacement s. W is N.m W = F.s 1 Joule (J) = (1N.m)

  6. W > 0 W < 0 W = 0

  7. Work and Kinetic Energywork-energy theorem W = Kf - Ki

  8. Gravitational Potential Energy (Near Earth’s surface) U = mgy

  9. Uel = (1/2) kx2

  10. Work-Energy Theorem Wtotal = Kf – Ki • Conservatives force Kf + Uf = Ki + Ui • Non-conservative forces Kf + Uf = Ki + Ui + Wother

  11. Off center collisions

  12. Suppose we have several particles A, B, etc., with masses mA, mB, …. Let the coordinates of A be (xA, yA), let those of B be (xB, yB), and so on. We define the center of mass of the system as the point having coordinates (xcm,ycm) given by xcm = (mAxA + mBxB + ……….)/(mA + mB + ………), Ycm = (mAyA + mByB +……….)/(mA + mB + ………).

  13. v = rω atan = rα arad = rω2

  14. Kinetic Energy of Rotating Rigid BodyMoment of Inertia KA = (1/2)mAvA2 vA = rAω vA2 = rA2ω2 KA = (1/2)(mArA2)ω2 KB = (1/2)(mBrB2)ω2 KC = (1/2)(mCrC2)ω2 .. K = KA + KB + KC + KD …. K = (1/2)(mArA2)ω2 + (1/2)(mBrB2)ω2 ….. K = (1/2)[(mArA2) + (mBrB2)+ …] ω2 K = (1/2) Iω2 I = mArA2 + mBrB2 + mCrC2) + mDrD2 + … Unit: kg.m2

  15. Rotation about a Moving Axis • Every motion of of a rigid body can be represented as a combination of motion of the center of mass (translation) and rotation about an axis through the center of mass • The total kinetic energy can always be represented as the sum of a part associated with motion of the center of mass (treated as a point) plus a part asociated with rotation about an axis through the center of mass

  16. Total Kinetic Energy Ktotal = (1/2)Mvcm2 + (1/2)Icmω2

  17. Rotation about a moving axis

  18. Conservation of angular momentum When the sum of the torques of all external forces acting on a system is zero, then THE TOTAL ANGULAR MOMENTUMIS CONSTANT (CONSERVED)

  19. The professor as figure skater? • It seems that danger to the instructor is proportional to interest in any given demonstration.

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