Download Announcements Torque Examples of Lever Arm Example: Pedaling

2/20/15 Announcements
•  Today: Torque, Angular Momentum
•  Wednesday: Gravity
•  Reading: Chapter 10, focus on figs. 10.3,
10.17, & 10.31
•  Reminder: Midterm #1 is on Friday!
–  Topics list is posted on class website
–  Bring pencil, eraser, calculator, and scantron 882E
Examples of Lever Arm
Torque
•  Torque is the rotational analog of force.
•  Depends on:
–  Magnitude of Force
–  Direction of force
–  Lever arm
•  torque = lever arm x force
•  Units of N!m
Example: Pedaling a Bicycle
•  Lever arm is amount of perpendicular
distance to where the force acts.
Revisiting Newton’s Laws
1: Need a linear force to change an object’s
linear motion " Need a torque to change an
object’s rotational motion
•  Equilibrium:
Example: See-Saw Balancing
4m
?m
–  Linear: ΣF = 0
–  Rotational: Στ = 0
2: Translational acceleration ~ force, and ~
1/mass " Angular acceleration ~ torque,
and ~ 1/rotational inertia
1 2/20/15 Ranking
•  Which meter
stick requires
the most
torque to hold
up the
weight?
Announcements
•  Today: Finish up rotation
•  Friday: Midterm #1!
•  No reading!
Center of Mass
Example
•  Average position of all the mass in an
object is called the center of mass (CM) of
object.
•  Average position of the weight distribution
is called the center of gravity (CG).
•  When gravity is constant (usually the
case), these two locations are the same.
•  Three trucks are parked on a slope. Which
truck(s) tip over?
Angular Momentum
Conservation of Angular Momentum
•  Recall: Linear momentum = mass x
velocity
•  Angular momentum = rotational inertia x
rotational velocity
If no external net torque acts on a rotating
system, then the angular momentum of that
system remains constant.
L=Iω
•  Need an impulse to change linear
momentum " need a torque to change
angular momentum!
2 2/20/15 Examples
•  Conservation of angular momentum plays
a big role in astronomy, because it relates
tangential speed (or orbital speed) to
radius (or orbital distance).
•  Formation of stars, planetary systems, and
galaxies
•  Moon’s orbit around the Earth
Example: Merry-go-round
•  What is the angular momentum of our 75
kg person going 3 m/s on the merry-goround with radius of 2 m?
Angular Momentum
•  Special case: for an object that is small
relative to its axis of rotation (planet in its
orbit, bug on a turntable)
Angular momentum L = mvr
Units: kg m2 /s
Centripetal Force
•  Centripetal means “towards the center.”
Whenever an object
moves along a
circular path, there
must be a force on
that object in the
direction of the
center of the circle.
•  In such a case, the force is said to be centripetal
Centripetal Force
Example: The spin cycle!
•  Any force directed toward a fixed center is
called a centripetal force.
–  Centripetal means “center-seeking” or “toward
the center.”
F = mv2/r
r = radius of circle
v = tangential velocity
3 2/20/15 Example
Centrifugal Force (by XKCD)
You are riding at the very edge of a merrygo-round with a radius of 2 m. Your friend
runs alongside, pushing the merry-go-round
so that it’s tangential speed is 3 m/s.
a.  What force is keeping you from sliding
off?
b.  If you have a mass of 75 kg, what is the
strength of that force?
4