Lecture 20
pls20.1
Rotational Kinematics II
Media: 1.
Solid disc
Clicker questions 1 – 3
.
1.
Tangential Variables
Consider an object rotating with angular velocity
dt
d
θ
ω
=
and angular acceleration
dt
d
ω
α
=
.
Now consider a particular point on the object, as illustrated in either
picture above.
Because the point moves in a circle, its velocity is
tangent to the circle.
The magnitude of velocity of the point is related
to the angular velocity
ω
via
ω
r
v
T
=
where here all variables are magnitudes.
The
T
subscript is not really
necessary, but it reminds us that the velocity is tangential to the circle
that describes the motion.
Let’s consider the time derivative of this equation,
dt
d
r
dt
dv
T
ω
=
.
1
s
1
r
.
2
s
2
r
θ
θ
T
v
T
v
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Lecture 20
pls20.2
Now
α
ω
=
dt
d
and we identify
T
T
a
dt
dv
≡
as the tangential component of
the acceleration, and so we have
α
r
a
T
=
2.
Centripetal and Tangential Acceleration (Components)
Because the point is moving in a circle it also has, at any point in time, a
centripetal component of acceleration (as we discussed in the context
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 Fall '11
 KODERA
 Physics, Acceleration, Angular Acceleration

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