2.3 
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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
Rolling
Rolling motion A rolling wheel has both linear and angular velocity. If the wheel is not slipping, the two velocities are related by geometry, because the circumference of a circle is 2π times the radius r. A wheel rotates through an angle of 2π radians (a full rotation) as it moves forward by a distance of 2πr (one circumference ).Radius and the circumference of a circle
What is the linear velocity? The linear velocity is the circumference divided by the time it takes to make one turn, i.e., v = 2πr/t. For one rotation, the quantity 2π/t is the angular velocity ω. The linear velocity is therefore equal to ω multiplied by the radius r. Linear and angular velocity are related to each other by the equation:
Linear velocity and angular velocity
(2.15) v=ωr
v  = linear velocity (m/s)
ω  = angular velocity (rad/s)
r  = radius (m)
Linear velocity
from angular velocity
Why did old bicycles have such large wheels? Why did old bicycles have such large wheels? The radius, r, that appears in equation 2.15 means that larger wheels have a higher linear velocity than smaller wheels for a given angular velocity. Early bicycles had very large wheels because the larger wheels would create a higher linear velocity. Unfortunately, they were very difficult to ride and quite unstable! Modern bicycles use gears and chains so that the pedals can turn at a different angular velocity from the wheels.
Linear speed of a rolling wheel
Test your knowledge A wheel is rolling at a linear velocity of 25 m/s. If the radius of the wheel is decreased, and the linear velocity remains the same, what does this indicate about the angular velocity of the smaller wheel?
  1. It remains unchanged
  2. It increases
  3. It decreases
  4. Not enough information to answer
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Solved Problem 2.7: Rotation of rolling wheel
A car has wheels with a radius of 30 cm. What is the angular velocity of the wheels in radians per second (rad/s) and revolutions per minute (rpm) when the car is moving at 30 m/s (67 mph)?

Asked: You are asked for the angular velocity ω in two units: rad/s and rpm.
Given: Radius r = 0.3 m
Velocity v = 30 m/s
Relationships: Linear velocity v = ωr.
One revolution is 6.28 radians.
There are 60 seconds in a minute.
Solution: ω = v/r = (30 m/s)/(0.3 m) = 100 rad/s.
Converting to units of rpm: ω = (100 rad/s)×(60 s/min)×(1 revolution/6.28 rad) = 955 rpm
Answer: ω = 100 rad/s = 955 rpm

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