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PROBLEM 11.173
A particle moves along the spiral shown. Determine the magnitude
of the velocity of the particle in terms of b, , and .
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PROBLEM 11.174
A particle moves along the spiral shown. Determine the magnitude of the
velocity of the particle in terms of b, , and .
PROBLEM 11.175
A particle moves along the spiral shown. Knowing that
is
constant and denoting this constant by ,
determine the
magnitude of the acceleration of the particle in terms of b,
, and
.
PROBLEM 11.176
A particle moves along the spiral shown. Knowing that
is constant and
denoting this constant by ,
determine the magnitude of the acceleration of
the particle in terms of b, , and
.
PROBLEM 11.177
The motion of a particle on the surface of a right circular cylinder is
defined by the relations R A, 2,t
and sin 2 ,zB nt
where A and
B are constants and n is an integer. Determine the magnitudes of the
velocity and acceleration of the particle at any time t.
PROBLEM 11.178
Show that
sin
rh
knowing that at the instant shown, step
AB of the step exerciser is rotating counterclockwise at a
constant rate
.
PROBLEM 11.178 (Continued)
PROBLEM 11.179
The three-dimensional motion of a particle is defined by the relations (1 ), 2 ,
t
R
Ae t
and
(1 ).
t
zB e
Determine the magnitudes of the velocity and acceleration when (a) t 0, (b) t .
PROBLEM 11.180*
For the conic helix of Problem 11.95, determine the angle that the osculating plane forms with the y axis.
PROBLEM 11.95
The three-dimensional motion of a particle is defined by the position vector
r
(Rt cos
n
t)
i
ct
j
(Rt sin
n
t)
k
. Determine the magnitudes of the velocity and acceleration of the particle.
(The space curve described by the particle is a conic helix.)
PROBLEM 11.180* (Continued)
