Transcript Impulse (in rotations)

IMPULSE
On a secret mission…
… to change equilibrium states!
EXTENSION to ROTATIONS
Translation concepts:
• Mass
Equivalent Rotation concepts:
• ??? (define it)
• Linear velocity
• ??? (define it)
• Linear momentum
• ??? (define it)
• Force
• ??? (define it)
• Impulse equation
• ??? (define it)
EXTENSION to ROTATIONS
Translation concepts:
• Mass
• Linear velocity
Equivalent Rotation concepts:
• Moment of inertia (mass
and its distribution relative
to the axis of rotation)
• Angular velocity
• Linear momentum
• Angular momentum
• Force
• Torque
HOW DOES IT WORK?
EQUILIBRIUM IN TRANSLATIONS
• The ability of an object to
stay @ rest depends on its
mass:
• Inertia is measured by mass.
• Symbol for mass: m
• Mass is a scalar.
EQUILIBRIUM IN ROTATIONS
• The ability of an object to
be put into rotations (from
rest) depends on mass and
mass distribution:
• Inertia is measured by
moment of inertia.
• Symbol for moment of
inertia: I
• Moment of inertia is a
scalar.
HOW DOES IT WORK?
EQUILIBRIUM IN TRANSLATIONS
• Once moving, the ability of
an object to stay in uniform
linear motion depends on
its linear momentum:
• Inertia is measured by linear
momentum.
• Symbol for linear
momentum: p
• Linear momentum is a
vector.
EQUILIBRIUM IN ROTATIONS
• Once moving, the ability of
an object to stay in uniform
rotational motion depends
on its angular momentum:
• Inertia is measured by
angular momentum.
• Symbol for angular
momentum: L
• Angular momentum is a
vector.
HOW DOES IT WORK?
EQUILIBRIUM IN TRANSLATIONS
• Equation for linear
momentum: p = m∙v
• Linear momentum is a
vector.
• In one dimension (1D),
vector directions are given
by “+” or “-”, “up” or
“down”, and by (opposite)
cardinal points.
EQUILIBRIUM IN ROTATIONS
• Equation for angular
momentum: L = I∙ω
• Angular momentum is a
vector.
• In rotational motion, the
direction of vectors is said
to be “clockwise” or
“counterclockwise.”
HOW DOES IT WORK?
AGENTS IN TRANSLATIONS
• To produce a change
between equilibrium states,
impulse must be produced.
• In translations, impulse
depends on force and
interaction time:
• I = F·Δt
• Force is a push or a pull in a
direction.
AGENTS IN ROTATIONS
• To produce a change
between equilibrium states,
impulse must be produces.
• In rotations, impulse
depends on torque and
interaction time:
• I = τ∙Δt
• Torque is force applied with
leverage – force applied at a
distance from the axis of
rotation.
EXTENSION to ROTATIONS
TRANSLATION CONCEPTS:
• Inertia: mass m
ROTATION CONCEPTS:
• Linear velocity: v
• Angular velocity: ω (Greek
letter lowercase omega)
• Angular momentum: L
𝐿 =𝐼∙𝜔
• Torque: τ (Greek letter
lowercase tau)
• 𝜏 = 𝐹 ∙ 𝑑 (at 90° angle)
• Impulse: I
𝐼 = 𝜏 ∙ ∆𝑡
• Linear momentum: p
𝑝=𝑚∙𝑣
• Force: F
• Impulse: I
𝐼 = 𝐹 ∙ ∆𝑡
• Inertia: moment of inertia I
THE END
© Lilian Wehner