PH 1110
Term A10
STUDY GUIDE 2:
2-D Motion, Newton's Laws of Motion
Objectives
10. Solve problems concerning the displacement, velocity, and acceleration of a particle moving along a
circular path.
11. State Newton's first, second, and third laws.
Be able to identify the reaction force to any force acting
on a body.
Distinguish between mass and weight.
12. Draw a diagram representing a body isolated from its environment in an inertial coordinate frame,
indicate with arrows all forces that act on it, and identify the source of each force.
Such a diagram is
called a "free-body diagram
".
13. Apply Newton's laws to determine the acceleration of an object and present a clear, concise written
solution of the problem.
14. Solve more complicated Newton's 2nd law problems, particularly those involving friction forces
and/or circular motion.
Suggested Study Procedure for Chapter 3.
Study
Secs. 3.1, 3.2, and 3.4.
Study
particularly Examples 1ac, 2b, 3, 4, 11, 12.
Answer
Discussion Questions 1, 2, 4, 12.
Do
Exercises 3bc, 7, 31, 33, 35.
A. In Secs. 3.1 and 3.2 you find how displacement, velocity, and acceleration are handled when motion is
NOT constrained to lie along a single straight-line direction.
Note that we simply apply the machinery
of one-dimensional motion and of vectors in order to generalize to ANY possible motion.
1. In multi-dimensional cases, remember that "constant velocity" means constant in DIRECTION as
well as MAGNITUDE (the object moves in a straight line at a constant speed -- this is quite
uncommon as far as the motion of "everyday" objects is concerned).
An object that changes
direction under ANY circumstances is accelerating.
2. Similarly, "constant acceleration" means that the acceleration vector is constant in magnitude AND
direction throughout the motion.
When acceleration is not zero, the velocity vector MUST
necessarily be changing with time, either in magnitude, in direction, or both.
3. The component of acceleration perpendicular to
v
changes the DIRECTION but not the magnitude
of
v
.
The component of acceleration parallel to
v
changes the MAGNITUDE of
v
(the speed)
but not the direction.
Try applying this rule to the various examples in Chapt. 4 and see if it
doesn't help demystify seemingly complex two- and three-dimensional motions.
B. Sec. 3.3 introduces an important special case of motion where the vertical component of acceleration is
CONSTANT and the horizontal component is ZERO.
Provided that we can ignore air friction, this
case describes the motion of objects tossed around just above the Earth's surface.
Notice how
following the Problem-Solving Strategy (p. 82) applies to the Examples, Exercises, and Problems.
C. Sec. 3.4 introduces another VERY IMPORTANT special case of motion – namely, circular motion at