10 Questions
Uniform circular motion is the projection of ______ motion onto a diameter.
simple harmonic
The displacement of the marker is given by x=______, where R is the distance of the marker from the axis of rotation.
Rcos(θ)
The maximum displacement of the motion is called the ______ of the motion and is represented by the symbols A and B that in this picture equal R.
amplitude
The equation for simple harmonic motion can be derived by projecting the motion of the marker upon the diameter AB, the displacement is given relative to the center of the path O and is represented by ______.
x-OC
The motion of the marker in a horizontal plane, viewing the turntable edge-on, will seem to be moving back and forth along a ______.
line
What is the name given to the motion which is the projection of uniform circular motion onto a diameter?
Simple harmonic motion
How is the displacement of the marker represented in the context of the motion?
x = Rcosθ
What term is used to denote the maximum displacement of the motion?
Amplitude
What is the equation for simple harmonic motion derived by projecting the motion of the marker upon the diameter AB?
x = Rcosθ
What type of motion is the projection of uniform circular motion onto a diameter?
Simple harmonic motion
Study Notes
- The text discusses analyzing the periodic motion of a marker on a circular object rotating about a vertical axis at a uniform rate.
- The observed motion of the marker in a horizontal plane is called simple harmonic motion and is the projection of uniform circular motion onto a diameter.
- The displacement of the marker relative to the center of rotation is represented by x-OC and can be expressed as x = Rcosθ, where R is the distance of the marker from the axis of rotation.
- The maximum displacement of the motion is called the amplitude of the motion, which is represented by symbols A and B in the text and is equal to R.
- The text mentions that Newton's Second Law of Conservation of Energy has been used to analyze oscillating systems like the spring-object system and simple pendulum, and now the focus is on analyzing the periodic motion of the circle.
Test your understanding of analyzing the periodic motion of a marker on a rotating circle in a horizontal plane. Explore the application of Newton's Second Law of Conservation of Energy and the principles of circular motion.
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