Transcript Chapter 13 - AJRomanello

Chapter 11
Rolling, Torque, and Angular
Momentum
Section 11.2 & 11.3
Rolling as Translation and Rotation
Combined & Kinetic Energy of Rolling
 Vcm = ωr
 K = ½ Iω2
 Combining the rotational and
translational kinetic energy to get
total kinetic energy we get:
 K = ½ mv2 + ½ Iω2
Section 11.4
The Forces of Rolling
 Friction and Rolling
 Remember acm = αr
 So a tangential frictional force will slow a
rotational object according to the equation:
 macm = mαr
Section 11.7 & 11.9
Angular Momentum & Rigid Bodies
 Linear Momentum – the product of
Mass and Velocity.
ρ = mv
 Angular Momentum (l) – the product
of Rotational Inertia and Angular
Velocity.
L = r x ρ = m(r x v)
L = Iω
The Relationship between Linear
and Angular Momentum
 Linear momentum = ρ
 Angular momentum = L
 L = ρxr where r is the radius of
rotation.
Changing of Angular Momentum
(Impulse)
 In a linear system the change in
momentum, known as impulse, was
given by:
FΔt = mΔV
 In an angular system the change in
angular momentum is given by:
FrΔt = IΔω
or
ΤΔt = IΔω
Section 11.11
Conservation of Angular Momentum
 Just as Linear Momentum was
conserved, Angular Momentum must
also be conserved in a closed system.
 So:
 Iiωi = Ifωf
Chapter 12
Equilibrium and Elasticity
Section 12.2 & 12.3
Conditions of Equilibrium
 ∑Fx = zero
 ∑Fy = zero This is Translational
 ∑Fz = zero
Equilibrium!
 ∑Text = zero
This is Rotational
Equilibrium!
Section 12.4
Center of Gravity
 The gravitational force on a body, Fg,
effectively acts on a single point,
called the center of gravity.
 If Fg is the same for all elements of a
body, then the body’s center of
gravity is coincident with its center of
mass.
Section 12.5
Some Examples of Static Equilibrium
 Car on a Bridge
 A 2000 kg car rests, 50 meters from one
end of a 100,000 kg uniform bridge which is
300 m long and has supports at 100 and
200 m. What force acts on each support?
 People on a Porch Swing
 Suzie (m = 50 kg) and Johnny (m = 65 kg)
are sitting on either end of a 1.5 m, 80 kg
uniform swing which is held up by two
chains. What is the force on each chain?
Section 12.7
Elasticity
 Tension – the stretching of an object
by force (outward pull)
 Compression – The compacting of an
object by force (inward push)
 Tension and Compression are at right
angles to the plane of the object.
 Shearing – is also a stress, however it
is in the plane of the area rather than
at right angles to it.