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
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


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


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

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)

WWW.XKCD.COM
11.7 CONSERVATION OF ANGULAR
MOMENTUM

If no unbalanced external torque acts on a
rotating system, the angular momentum is
constant
Iw=Iw
```