2D Particle Kinematics – Motion in
nt
coordinates
(1) Velocity:
ˆ
t
υ
=
G
Direction  velocity is tangent to the path, so
G
is directed along the +
t
axis.
Magnitude (speed) 
ds
dt
=
where
s
is the actual traveling distance along the trajectory
(2) Acceleration:
22
ˆ
ˆ
tn
t
aa
ta
n a a a
=+
⇒
=
+
G
n
Tangential acceleration – change in magnitude of velocity (speed):
t
d
a
dt
=
.
Normal acceleration – change in direction of velocity:
2
n
a
R
=
R
= radius of curvature
−
Circular motion
2
radius of the circle
t
nr
a
d
R
d
a
dt
R
=
=
=
=
Uniform circular motion:
υ
= constant
2
: period in sec,
: frequency in
0
2
2
4
4
Hz
t
a
d
a
R
Rf
T
R
R
f
R
Tf
T
π
υπ
=
==
=
=
NOTE: In circular motion, the normal acceleration is always pointing toward the center of the circle,
so it is also referred to as the centripetal acceleration or radial acceleration (
a
rad
).
Example
The Ferris wheel has a 12 m radius and rotates clockwise as shown. (a) If the wheel is rotating at a constant rate with
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 Spring '08
 TSChang
 Physics, Acceleration, Rotation, Velocity, normal acceleration

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