What is the centripetal acceleration of the end of the rod?

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SUMMARY

The discussion centers on calculating the centripetal acceleration of the end of a rotating rod, specifically one that is 15.3 cm long and rotates at a speed of 2010 m/s. Participants clarify that the speed mentioned refers to tangential velocity, not angular velocity. The correct approach to find centripetal acceleration involves using the formula \( a_c = \frac{v^2}{r} \), where \( v \) is the tangential velocity and \( r \) is the radius. For this rod, the radius is 7.65 cm, leading to a definitive calculation of centripetal acceleration.

PREREQUISITES
  • Understanding of centripetal acceleration formula: \( a_c = \frac{v^2}{r} \)
  • Knowledge of tangential velocity and angular velocity distinctions
  • Familiarity with SI units, particularly for speed and acceleration
  • Basic geometry concepts related to radius and diameter
NEXT STEPS
  • Calculate centripetal acceleration using the formula \( a_c = \frac{v^2}{r} \) with different values of \( v \) and \( r \)
  • Explore the relationship between angular velocity and tangential velocity in rotational motion
  • Research the implications of varying the radius on centripetal acceleration
  • Study real-world applications of centripetal acceleration in engineering and physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators seeking to clarify concepts of centripetal acceleration and tangential velocity.

Heidikins07
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Here is the homework question...

According to the Guinness Book of World Records, the highest rotary speed ever attained was 2010m/s(4500mph). The rotating rod was 15.3cm(6in.) long. Assume the speed quoted is that of the end of the rod. What is the centripetal acceleration of the end of the rod?

So I think since they say rotary speed they are talking about angular velocity here. so i would say angular velocity (w) = 2010m/s. Is this correct? or is it tangential velocity (v) = 2010m/s?



okay...does this mean it's rotating about the middle or about the end? (diameter being 15.3 radius being 7.65) orrrrrr (radius being 15.3 and diameter being 30.6) ??
 
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Heidikins07 said:
So I think since they say rotary speed they are talking about angular velocity here. so i would say angular velocity (w) = 2010m/s. Is this correct? or is it tangential velocity (v) = 2010m/s?
What is the SI unit of angular speed?


okay...does this mean it's rotating about the middle or about the end? (diameter being 15.3 radius being 7.65) orrrrrr (radius being 15.3 and diameter being 30.6) ??

Well, nothing has been stated specifically. If this written homework, you could check with your teacher. If this is one of those computerised tests, which gives you three chances at the right answer, then use 15.3 cm as the radius in your first try.
 
yea, it's written homework. so i did it both ways and I am just gunna ask my teacher! thanks tho! Ü
 

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