Angular acceleration of a blender

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SUMMARY

The angular acceleration of a blender's blades, which rotate at 6100 RPM, is calculated to be -489286 rad/s². The initial angular velocity (wI) is determined to be 2.3 x 10^6 rad/s, while the final angular velocity (wf) is 0 rad/s after the blades come to rest in 4.7 seconds. The formula used for angular velocity is w = 2πf, where f is the frequency in revolutions per second. The conversion from RPM to radians per second is crucial for accurate calculations.

PREREQUISITES
  • Understanding of angular velocity and acceleration concepts
  • Familiarity with the formula w = 2πf for angular velocity
  • Basic knowledge of unit conversions between RPM and radians per second
  • Ability to perform calculations involving time and angular motion
NEXT STEPS
  • Research the relationship between RPM and radians per second for various mechanical systems
  • Learn more about angular acceleration and its applications in rotational dynamics
  • Explore the effects of friction and other forces on angular motion
  • Study the principles of rotational kinematics and dynamics in engineering contexts
USEFUL FOR

Mechanical engineers, physics students, and anyone interested in the dynamics of rotating systems will benefit from this discussion.

daltomagne
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The blades in a blender rotate at a rate of 6100rpm. When the motor is turned off during operation, the blades slow to rest in 4.7s
What is the angular acceleration as the blades slow down?
f=6100rpm=366000rps
dt=4.7s

w=2(pi)f
angular acceleration=dw/dt

w=2(pi)3.66*10^5=2.3*10^6 rad/s
wI=2.3*10^6 rad/s
wf=0
angular a=(0-(2.6*10^6))/4.7s=-489286 rad/s2


I thought I was doing it right, but it appears not.
 
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6100 rpm is not 366000 rad/s.

I'm not sure what w=2(pi)f means?
 

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