Honors Physics Review 2 Chapter 4 - 7

Newton’s Three Laws of Motion 1st: When An object with no net force acting on it remains at rest or moves with constant velocity in a straight line.direction. 3rd: When one object exerts a force on a second object, the second object also exerts a force on the first object that is equal in magnitude but opposite in direction.

Tension Tension is along the line. Tension points away from the object. T

Normal Force (N or FN) Normal force points from surface to object. Normal force is always perpendicular to the surface in contact. (Normal = perpendicular) If there is no tendency for the object to go into the surface, there is no normal force. Fapp N N N

Weight and Apparent Weight Weight is force of gravity of Earth pulling on the object. N Apparent weight is the normal force or tension. T

Free-Body Diagram (Force Diagram) Draw all the forces acting on the object of consideration. Ignore all forces the object acting on other objects (reaction forces) Draw all forces starting from center of the object for simplicity. (frictional force normally is drawn at surface of contact.) T N W f

Adding Vectors: Head-to-Tail Head-to-Tail method: B A Example: A + B Draw vector A Draw vector B starting from the head of A A+B B The vector drawn from the tail of A to the head of B is the sum of A + B. A

Vector Components y a ay x ax  is the angle between the vector and the +x axis.  x ax

Vector magnitude and direction y ay a Vector magnitude and direction  ax x The magnitude and direction of a vector can be found if the components (ax and ay) are given:  is the angle from the +x axis to the vector.

Friction Friction: force opposing the motion or tendency of motion between two rough surfaces that are in contact Static friction is not constant and has a maximum: Kinetic (or sliding) friction is constant:

Equilibrium and Equilibrant Force Concurrent forces: forces acting on the same object at the same time. Equilibrium: Fnet = 0 Equilibrant Force: A force that produce equilibrium when applied to an object.

Independence of Motion From observation: The horizontal motion and the vertical motion are independent of each other; that is, neither motion affects the other. Connection: Both horizontal and vertical motions are functions of time. Time connects the two independent motions. Though these two motions are independent, they are connected to each other by time.

Initial Velocity Initial velocity: vi at angle i with the horizontal viy vi i x vix

Projectile Motion Breakdown Projectile: Object launched into the air Horizontal: Constant velocity

Projectile Motion Breakdown (2) Similarly, Vertical: Constant acceleration (ay = g, downward) ay = g if downward is defined as +y direction ay = -g if upward is defined as +y direction

Symmetry of Trajectory (2) Velocity at any moment is tangent to the actual path. Velocity is horizontal at the top of the trajectory. v vy vx vx vy v

Projectile Motion Minimum speed at top, but vy = 0 x y Projectile Motion Minimum speed at top, but vy = 0 vx = vix = vi cos i Maximum Height is Horizontal Range Only when initial and final heights are the same. Equation of Path

Centripetal Acceleration and Force v Direction of acceleration is always toward the center of circle (or circular arc) a a v a v for uniform circular motion at any time.

Direction of Acceleration a in the same direction as v:  Speed: increases a opposite to v:  Speed: decreases a  v:  Speed: does not change  Direction of velocity: changing

Uniform Circular Motion Period: Time for one complete cycle Frequency: Number of cycles per unit time

Relative Velocity VA,B Velocity of A relative to B Velocity of A measured by B Velocity of A at reference frame B

Kepler’s Three Laws of Planetary Motion 1st: The paths of the planets are ellipses with the center of the sun at one focus. 2nd: An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Thus, planets move fastest when closest to the sun slowest when farthest away. 3rd:

Newton’s Law of Universal Gravitation m1 and m2 are masses of the two objects r = distance between m1 and m2, center to center Gravitational force is always attractive, pointing from center to center.

m r Using Newton M