Page 94 - Dynamics of Mechanical Systems

0593_C03_fm Page 75 Monday, May 6, 2002 2:03 PM

Kinematics of a Particle 75

P3.5.2: Consider the Earth to be a sphere with a radius of 3960 miles. Let P be a point on
the surface of the Earth at a latitude of 40˚, as represented in Figure P3.5.2. With the Earth
rotating on its axis one revolution per day, determine the magnitudes of the velocity and
acceleration of P.

N
P
k

O 40°

FIGURE P3.5.2
A point P on the surface of the Earth. S

Section 3.7 Motion on a Circle
P3.7.1: A particle P is located on the rim of a flywheel as shown in Figure P3.7.1. If the
radius of the flywheel is 300 mm, and if the angular displacement θ, the angular speed
ω, and the angular acceleration α are as shown in the figure, determine the n and n
x y
components of the velocity and acceleration of P.

n y
P
300 mm
α = 10 rad/sec 2
θ = 30°
n
ω = 100 rpm x

FIGURE P3.7.1
A particle P on the rim of a flywheel.

P3.7.2: An automobile A is traveling around a horizontal curve with a radius of 1000 feet.
If the maximum radial acceleration is 0.6 g (where g = 32.2 ft/sec ), determine the maxi-
2
mum speed V of A.
P3.7.3: A pickup truck T travels around a 600-ft-radius curve at 35 mph. If the driver
brakes the truck at 5 ft/sec , determine the magnitude of the acceleration a of T. What is
2
the angle between a and the direction of travel of T?

Section 3.8 Motion in a Plane
P3.8.1: See Example 3.8.1, and suppose that for the fixed cam and follower of Figure 3.8.1
the following geometric and kinematic data are given:

a = 150 mm b = 100 mm and θ ˙ = 40 rpm