Keywords: Free Body Diagrams; Newton's Laws; Mechanics; Kinematics; Dynamics;
Planar Motion; Kinematics; Translational Motion; Graphs; Displacement; Circular
Motion; Centripetal Force;
OBJECTIVES:
*Draw a diagram of a particle representation of a body isolated from its
environment in an inertial reference frame; and (a) illustrate, with vectors, all
forces that act upon it; and (b) identify, by name, the source of each force
illustrated.
*Given the time-dependent position vector r(t) = x(t)i unit + y(t)j unta for a particle,
draw the particle's path in the plane.
*For a particle undergoing circular motion, draw a free-body diagram and identify
the interactions responsible for the centripetal force; these forces may be
gravitational forces or contact force exerted by another body.
*Search out the necessary conditions concerning radius, speed, and forces to solve
problems by applying Newton's second law to a particle undergoing circular
motion.
Comments: Perhaps at some time you have had occasion to swing a massive
object at the end of a rope. Maybe you have watched a parent swing a child
around by his outstretched arms or have been fortunate enough to watch an
athlete throw the hammer. Certainly you have heard or watched an automatic
washer go through a spin-dry cycle. How was this spinning drum with holes in
its periphery able to speed up the "drying" process? The clothes were too large to
pass through the holes in the drum and were "held" in a circular path but the
water droplets were small enough to pass through the holes. The water droplets
fly through the holes in a straight-line path and are then disposed of.In this
lesson, you will explore the nature of the forces responsible for circular motion.
You will also look into the motion of several bodies connected together, such as
a plow to a horse, a train to a locomotive, or a barge to a tugboat.
Enough of this physics where things move along straight lines only! We
know that most interesting real-life motions involve curves of many and varied
shapes. In this lesson, you will extend your understanding of kinematics from
one dimension to two dimensions. To accomplish this, you will combine your
knowledge of calculus and vectors with concepts like position, displacement,
velocity, speed, and acceleration.Two important applications that will be
utilized many times in later lessons are covered here. One is the motion of a
particle experiencing constant acceleration, e.g., a baseball in flight; and the other
is the motion of a particle in a circular path with a constant speed, e.g., an earth
satellite in circular orbit.Some of the material presented in this lesson is not
covered in the text, so you will need to pay particularly close attention to the
examples and problems in the syllabus.
PREREQUISITES: Adding and subtracting vectors, multiplying a vector by a scalar,
manipulating unit vectors, and finding the magnitude of a vector. Solving
kinematics problems in one dimension. Computing angles in radians . Identifying
forces acting on an object and drawing a free-body diagram of the object.
Distinguishing between inertial and non-inertial reference frames.
Thursday of the Fourth Week - First Hour Exam - February 5th - 80 points