Rotational Form of Newton's Second Law - Help

AI Thread Summary
To determine the torque required for a turntable to reach 33.3 RPM in 2 revolutions from rest, the moment of inertia (I) was calculated as 2.56x10^-3 kgm² using the formula I = 0.5MR². The discussion highlighted the importance of using the correct unit conversion for angular speed, clarifying that 3.49 rev/s should be expressed as 3.49 rad/s. Participants emphasized the need to incorporate angular displacement (θ) in the calculations, utilizing kinematic equations adapted for rotational motion. The final solution was reached by recognizing that θ equates to 2 revolutions, allowing for the accurate calculation of torque. The conversation concluded with the participant successfully solving the problem after addressing the unit conversion and understanding the role of angular displacement.
Quarkn
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Homework Statement



A turntable must spin at 33.3RPM (3.49 rev/s) to play an old fashioned vinyl record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 2 revolutions, starting from rest? The turntable is a uniform disk of diameter .305m and mass 0.22kg.


Homework Equations



I = 0.5MR²
\tau = \alphaI
\alpha = (ωf-ωi)/t

The Attempt at a Solution



I=(0.5)(0.22kg)(.1525²)=2.56x10^-3 kgm²
 
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Quarkn said:

Homework Statement



A turntable must spin at 33.3RPM (3.49 rev/s)...
There's a little problem with your conversion of units for ω. Instead of "rev/s", it should be 3.49 ___/s (?)
...to play an old fashioned vinyl record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 2 revolutions, starting from rest? The turntable is a uniform disk of diameter .305m and mass 0.22kg.


Homework Equations



I = 0.5MR²
\tau = \alphaI
\alpha = (ωf-ωi)/t

The Attempt at a Solution



I=(0.5)(0.22kg)(.1525²)=2.56x10^-3 kgm²
Yup, that's I.

Your book should have even more relevant equations for rotational motion. You want one that involves θ, so that you can use the information that it takes 2 revolutions to get the turntable up to speed. You can check in your textbook for the full list of equations.
 
Starting from rest at a point O, let's call it, the motor supplies a torque so that by the second time we pass O, the angular speed is 3.49 rev/s. Based on this, you can use one of the kinematics equations (re-vamped into their respective rotational forms) and then incorporate the mass of the disc to find the torque.
 
Redbelly98 said:
There's a little problem with your conversion of units for ω. Instead of "rev/s", it should be 3.49 ___/s (?)

Yup, that's I.

Your book should have even more relevant equations for rotational motion. You want one that involves θ, so that you can use the information that it takes 2 revolutions to get the turntable up to speed. You can check in your textbook for the full list of equations.

Yes, it is 3.49 rad/s, sorry :P

Anyways, I found out the answer. My problem was that I didn't know theta was used as the 2 revolutions.
 
Okay, glad it worked out.
 
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