Describe the motion of a particle on the rim of a rolling wheel of radius a, given by the position: x(t)=a(0-sin0), y(t)=a(1-cos6), where angle 0=mt is the angle of rotation of the wheel. The name of that trajectory is cycloid, and the inverted cycloid is the brachistochrone curve, the curve of fastest descent. a) Find the velocity and acceleration of the particle along x and y directions. b) At which times tn the particle is at rest? At which times T, the particle moves the fastest? (n=0,±1,±2,) c) What are the positions and accelerations of the particle at these times?
Describe the motion of a particle on the rim of a rolling wheel of radius a, given by the position: x(t)=a(0-sin0), y(t)=a(1-cos6), where angle 0=mt is the angle of rotation of the wheel. The name of that trajectory is cycloid, and the inverted cycloid is the brachistochrone curve, the curve of fastest descent. a) Find the velocity and acceleration of the particle along x and y directions. b) At which times tn the particle is at rest? At which times T, the particle moves the fastest? (n=0,±1,±2,) c) What are the positions and accelerations of the particle at these times?
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Transcribed Image Text:Describe the motion of a particle on the rim of a rolling wheel of radius a, given by the position:
x(t)=a(0-sin0), y(t)=a(1-cos0), where angle 0=@t is the angle of rotation of the wheel. The name of that
trajectory is cycloid, and the inverted cycloid is the brachistochrone curve, the curve of fastest descent.
a) Find the velocity and acceleration of the particle along x and y directions.
b) At which times t, the particle is at rest? At which times Tn the particle moves the fastest? (n=0,±1,±2,)
c) What are the positions and accelerations of the particle at these times?
( πα, 2α)
x = a(0- sin 6)
y = a(1-cose)
a0
2πα
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