Inertia Question: Resolve the Wheel Motion

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SUMMARY

The discussion focuses on calculating the angular acceleration, angular speed, revolutions per second, total revolutions, and kinetic energy of a full metal wheel with a radius of 30 cm and a mass of 300 kg, using the moment of inertia formula I = 1/2 (mr^2) and an operating torque of 50 Nm over a duration of 1 minute. Key equations used include ω = 2π/T, s = 1/2(αt^2), and Ek = (Iω^2)/2. The final kinetic energy calculated was 7.5 kJ, which raised questions about the accuracy of the calculations and the conversion of energy units from mJ to Joules.

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Homework Statement



The full metal wheel of radius 30 cm, 300 kg of mass moment of inertia I = 1/2 (mr ^ 2) operating torque 50nm in time 1 min. Determine the angular acceleration, angular speed of wheel, revolutions per second, revolutions that the wheel makes to achieve this speed, kinetic energy.

Homework Equations



ω = 2∏/T, s=1/2(αt^2), Ek=(Iω^2)/2, I = 1/2 (mr ^ 2)

The Attempt at a Solution



First I can get ω, T=60sec, so ω=∏/30...

So I can get all of this using those few formulas, but in the end I get kinetic energy in mJ??
 
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the_man said:

Homework Statement



The full metal wheel of radius 30 cm, 300 kg of mass moment of inertia I = 1/2 (mr ^ 2) operating torque 50nm in time 1 min. Determine the angular acceleration, angular speed of wheel, revolutions per second, revolutions that the wheel makes to achieve this speed, kinetic energy.

Homework Equations



ω = 2∏/T, s=1/2(αt^2), Ek=(Iω^2)/2, I = 1/2 (mr ^ 2)

The Attempt at a Solution



First I can get ω, T=60sec, so ω=∏/30...

So I can get all of this using those few formulas, but in the end I get kinetic energy in mJ??
Why not get kinetic energy in Joules ?
 
SammyS said:
Why not get kinetic energy in Joules ?

I can get energy in Jules but then its very small number, but i don't get it why is a small number?
 
the_man said:

Homework Statement



The full metal wheel of radius 30 cm, 300 kg of mass moment of inertia I = 1/2 (mr ^ 2) operating torque 50nm in time 1 min. Determine the angular acceleration, angular speed of wheel, revolutions per second, revolutions that the wheel makes to achieve this speed, kinetic energy.

Homework Equations



ω = 2∏/T, s=1/2(αt^2), Ek=(Iω^2)/2, I = 1/2 (mr ^ 2)

The Attempt at a Solution



First I can get ω, T=60sec, so ω=∏/30...

So I can get all of this using those few formulas, but in the end I get kinetic energy in mJ??

The torque is acting for 1 minute; The given time of 1 minute is not the period of oscillation or rotation...
 
Okay. I got it! Now its Ek=7,5kJ
 
Perhaps you should elaborate on your calculations; To me, 7.5 kJ doesn't look right.
 
gneill said:
Perhaps you should elaborate on your calculations; To me, 7.5 kJ doesn't look right.

M=F*r
F=m*α
α=ω/T
Ek=(Iω^2)/2
 
the_man said:
M=F*r
F=m*α
α=ω/T
Ek=(Iω^2)/2

I see a collection of formulas, at least one of which is rather dubious, but no calculations. Can you show your numerical work and explain what the steps are that your taking?
 

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