1 - Science of Physics 2 - Forces and Motion Chapter 2 at a glance 2.1 - Motion 2.2 - Force, momentum, and Newton's laws 2.3 - Circular motion 2.4 - Solving harder physics problems 2.5 - Chapter review3 - Energy Transformations4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy
Notice from equation (2.16) that the centripetal acceleration goes down as the radius gets larger. The larger the circle, the slower the velocity has to change direction, and the lower the centripetal acceleration. The centripetal acceleration goes up as the square of the velocity. That means it takes four times as great an acceleration to force an object that is moving twice as fast into the same radius of circle.
Imagine whirling a small weight around your head on a string. If the string broke, the weight would fly off and no longer move in a circle. This is a consequence of Newton's first law: a moving body will continue in a straight line if no net force acts on it. What direction will it travel? An object undergoing circular motion has a velocity that is tangential to the circle. If the string were to break, then the object would continue moving in the direction of its velocity—upwards in the illustration.
To understand circular motion, it is important to distinguish between vectors that are tangential and radial. A radial vector is directed along the radius of the circle. A tangential vector is directed perpendicular to the circle at any point along its circumference. For a circle, the radial and tangential vectors are always perpendicular to each other. In the physics of circular motion, the centripetal acceleration and force are always radial vectors, while the object's velocity is a tangential vector. Centripetal acceleration and force are therefore always perpendicular to the velocity of an object undergoing circular motion. 
What keeps the object in circular motion over your head? The string must exert an acceleration (or force) that continually bends the weight's direction of motion towards the center of the circle. In the illustration, the velocity of the object changes direction as it moves from point A to point B. The change in velocity is represented by the vector Δv, which is perpendicular to the direction of velocity. Since acceleration is the rate at which an object’s velocity changes, the 
