Circular Motion

# Circular Motion - very similar manner the acceleration of...

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Circular Motion Suppose the motion of an object as function of time can be described by the following relations: (8) The equations in (8) describe a periodic motion: the position of the object at time t and at time t + T are identical. The period of the periodic motion is obviously T. The path of this object will be circular. This can be easily verified by calculating the distance of this object to the origin: (9) Clearly, the distance of the object to the origin is constant (independent of time). See Figure 4.3. The velocity of the object can be easily calculated using the relations in eq.(8): (10a) (10b) The direction and magnitude of the velocity vector are: Figure 4.3. Definition of trajectory. (11) (12)

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Figure 4.4. Direction of velocity and acceleration. Equation (11) shows that the direction of the velocity is perpendicular to the position vector. In a
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Unformatted text preview: very similar manner the acceleration of the object can be calculated: (13a) (13b) The direction and magnitude of the acceleration vector are: (14) (15) Equation (14) shows that the direction of the acceleration is in the radial direction (opposite to the position vector). See also Figure 4.4. Note: Equation (12) shows that the magnitude of the velocity of the object is constant (independent of time). Equation (11) shows that only its direction changes with time. Note: Equation (15) shows that the acceleration is non-zero. It is clear that this non-zero acceleration does not change the magnitude of the velocity, but it changes its direction. The acceleration will be non-zero if either the magnitude or the direction of the velocity changes....
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Circular Motion - very similar manner the acceleration of...

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