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Chapter 9: Circular Motion Chapter 10: Center of Gravity Chapter 11: Rotational Mechanics

Chapter 9: Circular Motion Chapter 10: Center of Gravity Chapter 11: Rotational Mechanics. Conceptual Physics Bloom High School Barry Latham, M.A.Ed. 9.1 Important Distinctions. Axis- the center point of a turning object Rotation- spinning about an internal axis Earth spinning once per day

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Chapter 9: Circular Motion Chapter 10: Center of Gravity Chapter 11: Rotational Mechanics

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  1. Chapter 9: Circular MotionChapter 10: Center of GravityChapter 11: Rotational Mechanics Conceptual Physics Bloom High School Barry Latham, M.A.Ed.

  2. 9.1 Important Distinctions • Axis- the center point of a turning object • Rotation- spinning about an internal axis • Earth spinning once per day • Revolution- spinning around an external axis • Earth orbiting around the Sun once per year

  3. 9.2 Rotational Speed • Linear Speed (Ch 2)- v=d/t • Always in a straight line • Rotational Speed (angular speed)- rotations per minute • rpm • PhET Ladybug Revolution 1.09 • Tangential Speed- moving along a circular path • Motion at any moment can be measured as a tangent to the circle • Proportional to the radial distance and rotational speed

  4. 9.3 Centripetal Force • Centripetal force- “center seeking” force • Force along a string that keeps a washer from flying off

  5. 9.4 Centripetal & Centrifugal Force • Centrifugal force- “center-fleeing” force • Causes an object to fly in a direction away from the center when no “connecting force” exists

  6. 10.1 Center of Gravity • Center of Gravity- the point of an object that displays projectile motion • Regardless of spinning and “projecting” through the air • PhET Gravity and Orbits 1.00 • http://www.youtube.com/watch?v=hqDhW8HkOQ8 • Rules of momentum still apply • A missile that is detonated mid air will have fragments that still follow the same projectile path

  7. 10.2 Center of Mass • Center of Mass- the average position for all of the mass in an object • Center of Gravity (CG)- nearly identical to center of mass • Only different if the gravitational field is different in different locations of the same object • Sears Tower has more gravity at the base than the top

  8. 10.3 Locating the CG • Balance an elongated object on a fulcrum point • Hang a string from different parts of the object and allow it to dangle • Mass doesn’t need to exist at the CG

  9. 10.4 Toppling • If the CG is above the area of support, the object won’t topple • As soon as the CG is outside of the “footprint” of the object, it will fall.

  10. 10.5 Stability • Unstable equilibrium- when any motion will allow the CG to become lower (fall closer to the floor) • Stable equilibrium- when any motion will attempt to raise the CG • Neutral equilibrium- when any motion will not change the CG height

  11. 10.6 CG of People • Typically 2-3cm below your navel, inside your body • Lower in women than men due to larger “lower body” • Higher in children due to proportionally larger head than adults

  12. 11.1 Torque • Torque- the force applied perpendicular to an rotating object multiplied by the distance to the axis of rotation • t=(F┴)(d) • More force leads to more torque • More distance from the axis leads to more torque • Example: Removing a nut from a bolt with your bare hands versus a pair of pliers • Example: Opening a door with the handle near the hinges versus far from the hinges

  13. 11.2 balanced Torques • If the value of (F┴)(d) for one object equals (F┴)(d) for another, then they are balanced • Example: See-Saw with a small kid far away versus a large kid up close

  14. 11.4 Rotational Inertia • Inertia (Ch 4)- an object keeps doing whatever it’s doing (moving or stationary) unless a force intervenes • Rotational Inertia- a rotating object keeps rotating at the same rate unless a force intervenes • Mathematical relationships vary • See Figure 11.14 • m=mass of object (kg) • r=distance from axis (m) • I=rotational inertia

  15. 11.6 Angular Momentum • Linear Momentum- p=mv, in a straight line, of course • Chapter 7 • Angular momentum- inertia of rotation about an axis • (Rotational inertia)(rotational velocity)=Iw • See Figure 11.14 for I value • w=rotational velocity (m/s) • Circular angular momentum=mvr • mv=linear momentum (kg m/s) • r=distance of object from axis (m)

  16. www.xkcd.com

  17. 11.7 Conservation of Angular Momentum • If no unbalanced external torque acts on a rotating system, the angular momentum is constant • Iw=Iw

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