2.3 
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Videos:
Interactive Simulations   Position and displacement in one dimension    Displacement and position in two dimensions    Solve v=dx/dt for dt    Velocity, position, and time (basic version)    Velocity, position, and time (more advanced version)    Acceleration (basic version)    Acceleration (more advanced version)    Static equilibrium    Static equilibrium and the lever    Newton's second law (basic version)    Newton's second law (more advanced version)    Circular motion interactive simulation    Orbits of the planets and dwarf planets    Orbits simulation Interactive Calculators   Speed calculator    Velocity calculator    Acceleration calculator    Velocity in accelerated motion    Average velocity calculator    Hooke's law calculator    Torque calculator    Rotational equilibrium and torque    Newton's second law calculator    Momentum calculator    Angular velocity    Linear velocity and angular velocity    Centripetal acceleration    Centripetal force    Law of universal gravitation calculator
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
2F: Circular motion
How are radius, velocity, acceleration, and force related in circular motion?
Many objects undergo circular motion: from spinning wheels to the orbits of satellites around the Earth. In order for an object to remain in circular motion, it must experience a centripetal force (or acceleration). In this investigation, you will explore the properties of circular motion at scales similar to a mass swung around horizontally at the end of a string.
Part 1: Directions of the velocity, force, and acceleration vectors

How to use the circular motion simulation
  1. Set m = 5.0 kg, r = 5.0 m, and v = 5.0 m/s.
  2. Play the simulation, and then pause it at various positions around the circle.
  3. Sketch the velocity, force, and acceleration vectors for at least five positions distributed around the circle.
  1. Which vector quantity or quantities are radial and which are tangential? Are the radial ones pointed inwards (towards the center) or outwards?
  2. Do the lengths of the velocity, acceleration, or force vectors change around the circle?
Circular motion interactive simulation In this interactive simulation, you will investigate how velocity, acceleration, and force vary when an object is undergoing circular motion.
Part 2: Approximating a mass swung overhead

  1. Set r = 1.0 m and m = 0.3 kg.
  2. Calculate the tangential velocity needed to spin the object around once per second, and enter that into the simulation.
  1. How much force is need to maintain this object in circular motion?
  2. Compare that force with the force required to hold the object motionless against the force of gravity.
  3. Lengthen the string to r = 2.0 m. Does it new require more or less force than before to maintain the object in circular motion with the same angular velocity?
Part 3: Variation of velocity with radius for circular motion

  1. Hold the force constant at 10 N and the mass constant at 2 kg but vary the length of the string from r = 1 m to 5 m.
  2. Record the velocity and radius for each case.
  1. Graph v against r and describe the shape of your graph.
  2. Graph v2 against r, describe the shape of your graph, and measure its slope.

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