Circular Motion of a 8.0cm CD: Finding Speed and Revolution Using Kinematics

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SUMMARY

The discussion focuses on calculating the speed and revolutions of a magnetic computer disk with an 8.0 cm diameter, which accelerates at 600 rad/s² for 0.5 seconds before coasting. The correct speed of the dot at t = 1.0 s is determined using the formula v = a * t, resulting in a final speed of 300 rad/s after the acceleration phase. The total number of revolutions can be calculated using the angular displacement during both the acceleration and coasting phases, leading to a comprehensive understanding of kinematic equations in circular motion.

PREREQUISITES
  • Understanding of angular acceleration and kinematics
  • Familiarity with circular motion concepts
  • Knowledge of basic physics formulas, including v = a * t
  • Ability to convert between linear and angular measurements
NEXT STEPS
  • Study the kinematic equations for rotational motion
  • Learn about angular displacement and its relationship to revolutions
  • Explore the conversion between linear speed and angular speed
  • Investigate practical applications of circular motion in engineering
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Students in physics, educators teaching kinematics, and engineers working with rotational systems will benefit from this discussion.

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A magnetic computer disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad/ s^2 for 1/2 s, then coasts at a steady angular velocity for another 1/2 s . a) What is the speed of the dot at t = 1.0 s?
b)Through how many revolutions has it turned?


for a) i kept getting the answer wrong:
i did :
d=8.0cm
so r=4.0 cm
ti=0s
tf=0.5s
a=600 rad/s^2

vi=(2)(pi)(4.0cm) / 1.0s

so; vi=25m/s


and for part b)
i think you have to use the kinematic equation after you get vi.. I'm not sure tho.. am i right?? please help. thanks in advance!
 
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For part a) What is the velocity after .5s - v=a*t
then coasts at a steady angular velocity for another .5 s - same Angular velocity as accelerated to
 

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