Page 32 - Dynamics of Mechanical Systems

0593_C01_fm Page 13 Monday, May 6, 2002 1:43 PM

Introduction 13

Y n θ
n y P(r,θ)

n
r
r

O θ
X
n
x
FIGURE P1.6.1
Polar coordinate system.

P1.6.2: Suppose the Cartesian coordinates (x, y, z) of a point P are (–1, 2, –5).

a. Find the cylindrical coordinates (r, θ, z) of P.
b. Find the spherical coordinates (ρ, φ, θ) of P.

P1.6.3: Suppose the cylindrical coordinates (r, θ, z) of a point P are (4, π/6, 2).

a. Find the Cartesian coordinates (x, y, z) of P.
b. Find the Spherical coordinates (ρ, φ, θ) of P.

P1.6.4: Suppose the spherical coordinates (ρ, φ, θ) of a point P are (7, π/4, π/3).

a. Find the Cartesian coordinates (x, y, z) of P.
b. Find the cylindrical coordinates (r, θ, z) of P.

P1.6.5: Consider the cylindrical coordinate system (r, θ, z) with z identically zero. This
system then reduces to the “polar coordinate” system as shown in Figure P1.6.1.

a. Express the coordinates (x, y) in terms of (r, θ).
b. Express the coordinates (r, θ) in terms of (x, y).

P1.6.6: See Problem 1.6.5. Let n and n be unit vectors parallel to the X- and Y-axes, as
x
y
shown. Let n and n be unit vectors parallel and perpendicular to the radial line as shown.
θ
r
a. Express n and n in terms of n and n .
θ
x
y
r
b. Express n and n in terms of n and n .
θ
r
y
x
Section 1.7 Systems of Units
P1.7.1: An automobile A is traveling at 60 mph.
a. Express the speed of A in ft/sec.
b. Express the speed of A in km/sec.