Linear momentum ( p ) will be maximally conserved when two particles moving towards one another with a constant velocity ( v ) along a straight line collide: p1i + p2i = p’1f + p’2f Things become somewhat more complicated when some measurable entity is maximized or minimized when it passes through some other entityContinue reading “MATHEMATICS: The Unit Circle, Sine, Cosine, and Tangent Functions”
Tag Archives: sin
AP PHYSICS: Trigonometry and Vector Components
Q: A charged species traveling at a constant velocity ( v ) through a magnetic field ( B ) will experience a force if the direction of motion is at a 900 angle with the B-field. How can trigonometry be used to quantify this phenomena? A: The magnetic force ( Fm ) on the chargedContinue reading “AP PHYSICS: Trigonometry and Vector Components”
AP PHYSICS: The Unit Circle and Basic Trigonometric Functions
Imagine a bat hitting a baseball head on. The ball-to-bat force pair created upon impact is unbalanced; thus, after impact, the ball will sail outward in the opposite direction. What if, however, the bat-to-ball collision occurred at an angle? How would the magnitude of force imparted to the ball change? Answers to these types ofContinue reading “AP PHYSICS: The Unit Circle and Basic Trigonometric Functions”
ENERGY AND MOMENTUM: A Windy Day at the Lake
Q: Wind blows a 43.0 kg raft across a lake at 1.1 m/s northward relative to the water underneath. It carries a passenger whose mass is 38.0 kg. The passenger begins to walk westward at 0.71 m/s. What is the final velocity of the raft relative to the water? A: We first determine the momentumContinue reading “ENERGY AND MOMENTUM: A Windy Day at the Lake”
KINEMATICS: The Speedboat Will Miss its Mark by What Distance?
A speedboat travels eastward at 80 knots (150 km/h) through a northward current of water moving 4.00m/s. Q1: What is the speedboat’s velocity vector relative to the starting port? What is the angle of travel? Q2: If the boat’s captain wanted the boat to travel due east without getting off course, how far off courseContinue reading “KINEMATICS: The Speedboat Will Miss its Mark by What Distance?”
ENERGY and MOMENTUM: What is the Final Velocity of the Ball?
Q: A 10 kg iron ball moves in an Eastward direction at 5.0 m/s. It collides with a 5.0 kg rubber ball moving Northward at 10 m/s. After the collision, the iron ball moves 60° East of North with a speed of 4.0 m/s. What is the velocity of the rubber ball after the collision?Continue reading “ENERGY and MOMENTUM: What is the Final Velocity of the Ball?”
RADIANT ENERGY: Wavenumber, Angular Frequency, and the Wave Nature of Light
Trigonometric functions such as sin ( θ ) and cos ( θ ) are commonly used to model the oscillating motion of traveling waves. In the diagram above, a complete wave cycle occurs from crest-to-crest, trough-to-trough, or along the x-axis as indicated by the blue line. Since the diagram above can be modeled with theContinue reading “RADIANT ENERGY: Wavenumber, Angular Frequency, and the Wave Nature of Light”
RENAISSANCE PHYSICS 