Inertia Question: Resolve the Wheel Motion

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In summary, 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. will achieve a speed of Revolutions per second by rotating 360 degrees in 1 minute. The wheel will achieve the speed by multiplying its mass by its moment of inertia and then dividing by the torque applied. The result is 7.5 kJ of kinetic energy.
  • #1
the_man
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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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  • #2
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 ?
 
  • #3
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?
 
  • #4
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...
 
  • #5
Okay. I got it! Now its Ek=7,5kJ
 
  • #6
Perhaps you should elaborate on your calculations; To me, 7.5 kJ doesn't look right.
 
  • #7
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
 
  • #8
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?
 

1. What is inertia?

Inertia is an object's resistance to change in its state of motion. In other words, it is the tendency of an object to maintain its current state of motion.

2. How does inertia affect a wheel's motion?

Inertia plays a significant role in a wheel's motion. The wheel will continue to move in a straight line unless acted upon by an external force. The greater the wheel's inertia, the more force is needed to change its motion.

3. How does the size and shape of a wheel affect its inertia?

The size and shape of a wheel can greatly impact its inertia. Generally, a larger wheel will have a greater inertia compared to a smaller wheel, as it has more mass and therefore requires more force to change its motion. A wheel with a larger diameter will also have a greater inertia compared to a wheel with a smaller diameter.

4. How does friction affect the inertia of a wheel?

Friction can reduce the inertia of a wheel by acting as an external force and slowing down its motion. This is why wheels on surfaces with higher friction, such as sand or gravel, will have a harder time maintaining their motion compared to wheels on smoother surfaces.

5. How can we use inertia to our advantage when designing wheels?

Inertia can be used to our advantage when designing wheels by choosing the appropriate size and shape for the desired motion. For example, larger wheels with greater inertia are more suitable for carrying heavy loads, while smaller wheels with lower inertia are better for quick and agile movements.

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