net force and free-body diagrams (Sections 2.2 and 2.3)
distinction between mass and weight (Sections 1.2 and 2.6)
gravitational forces, contact forces, and tension (Sections 2.6–2.8)
Newton's third law of motion; internal and external forces (Section 2.5)
Mastering the Concepts
Position <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663811/ch3_1.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> is the vector from the origin to an object's location. Its magnitude is the distance from the origin and its direction points from the origin to the object.
Displacement is the change in position:<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663811/ch3_2.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>. The displacement depends only on the starting and ending positions, not on the path taken. The magnitude of the displacement vector is not necessarily equal to the total distance traveled; it is the straight line distance from the initial position to the final position.
Average velocity is the constant velocity that would cause the same displacement in the same amount of time.
Velocity is a vector that states how fast and in what direction something moves. Its direction is the direction of the object's motion and its magnitude is the instantaneous
speed. It is the instantaneous rate of change of the position vector. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663811/ch3_4.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
The instantaneous velocity vector is tangent to the path of motion.
Average acceleration is the constant acceleration that would cause the same velocity change in the same amount of time.
Acceleration is the instantaneous rate of change of the velocity vector. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663811/ch3_6.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
Acceleration does not necessarily mean speeding up. A velocity can also change by decreasing speed or by changing direction. The instantaneous acceleration vector does
not have to be tangent to the path of motion, since velocities can change both in direction and in magnitude.
Interpreting graphs: On a graph of x(t), the slope at any point is vx. On a graph of vx(t), the slope at any point is ax, and the area under the graph during any time interval is the displacement Δ x during that time interval. If vx is negative, the displacement is also negative, so we must count the area as negative when it is below the time axis. On a graph of ax(t), the area under the curve is Δvx, the change in vx during that time interval.
Newton's second law relates the net force acting on an object to the object's acceleration and its mass:
The acceleration is always in the same direction as the net force. Problems involving Newton's second law— whether equilibrium or nonequilibrium—can be solved by treating the x- and y -components of the forces and the acceleration separately:
The SI unit of force is the newton: 1 N = 1 kg.m/s2. One newton is the magnitude of the net force that gives a 1-kg object an acceleration of magnitude 1 m/s2.
To relate the velocities of objects measured in different reference frames, use the equation
where <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663811/ch3_10.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> represents the velocity of A relative to C, and so forth.
