C HAPTER 9: C IRCULAR M OTION C HAPTER 10: C ENTER OF G RAVITY C HAPTER 11: R OTATIONAL M ECHANICS Conceptual Physics Bloom High School Barry Latham, M.A.Ed.

9.1 I MPORTANT D ISTINCTIONS 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

9.2 R OTATIONAL S PEED 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

9.3 C ENTRIPETAL F ORCE Centripetal force- “center seeking” force Force along a string that keeps a washer from flying off

9.4 C ENTRIPETAL & C ENTRIFUGAL F ORCE Centrifugal force- “center-fleeing” force Causes an object to fly in a direction away from the center when no “connecting force” exists

10.1 C ENTER OF G RAVITY Center of Gravity- the point of an object that displays projectile motion Regardless of spinning and “projecting” through the air PhET Gravity and Orbits Rules of momentum still apply A missile that is detonated mid air will have fragments that still follow the same projectile path

10.2 C ENTER OF M ASS 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

10.3 L OCATING 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

10.4 T OPPLING 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.

10.5 S TABILITY 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

10.6 CG OF P EOPLE 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

11.1 T ORQUE Torque- the force applied perpendicular to an rotating object multiplied by the distance to the axis of rotation  =(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

11.2 BALANCED T ORQUES 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

11.4 R OTATIONAL I NERTIA 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 m=mass of object (kg) r=distance from axis (m) I=rotational inertia

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

WWW. XKCD. COM

11.7 C ONSERVATION OF A NGULAR M OMENTUM If no unbalanced external torque acts on a rotating system, the angular momentum is constant I  =I 