CHAPTER 9: CIRCULAR MOTIONCHAPTER 10: CENTER OF GRAVITYCHAPTER 11: ROTATIONAL MECHANICSConceptual PhysicsBloom High SchoolBarry 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 Revolution- spinning around an external axis

Earth orbiting around the Sun once per year

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

9.3 CENTRIPETAL FORCE Centripetal force- “center seeking” force

Force along a string that keeps a washer from flying off

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

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

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

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

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.

10.5 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

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

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

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

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

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)

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11.7 CONSERVATION OF ANGULAR MOMENTUM If no unbalanced external torque acts on a

rotating system, the angular momentum is constant

Iw=Iw