Work done by a constant torque equation DOESN'T give me angular speed Help

In summary, the given values of torque, inertia, and angular displacement are used to calculate the angular speed of 38 rev/s. The conversion from rad/s to rev/s was necessary to obtain the correct answer.
  • #1
riseofphoenix
295
2
Number15.png


What is given:

Torque: τ = 34.5 N * m
Inertia: I = 0.130 kg * m2
Angular speed: ω = ?
Work done by a constant Torque: τΔθ = (1/2)Iωf2 [STRIKE]- (1/2)Iωi2[/STRIKE]
Angular displacement: Δθ = 17.1 rev/s = 107.442 rad/sτΔθ = (1/2)Iωf2
(34.5)(107.442) = (0.5)(0.130)ωf2
3706.765 = 0.065ωf2
57027.156 = ωf2
238.8 = ω

It's still wrong :(
 
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  • #2
Δθ is 17.1 revolutions. You need to convert that to radians.
 
  • #3
Make sure your angular displacement is in radians, not revolutions.
 
  • #4
Change 17.1rev's to ... radians's.
 
  • #5
3x should be enough :biggrin:
 
  • #6
Doc Al said:
3x should be enough :biggrin:

Wait what? :(
 
  • #7
grzz said:
Change 17.1rev's to ... radians's.

I just did and it's still wrong
 
  • #8
riseofphoenix said:
I just did and it's still wrong
Show what you did.
 
  • #9
If you show your work help may be given.
 
  • #10
Doc Al said:
Show what you did.

B]What is given:[/B]

Torque: τ = 34.5 N * m
Inertia: I = 0.130 kg * m2
Angular speed: ω = ?
Work done by a constant Torque: τΔθ = (1/2)Iωf2 [STRIKE]- (1/2)Iωi2[/STRIKE]
Angular displacement: Δθ = 17.1 rev/s
Conversion (17.1 x 2 x π) rad/s = 107.442

τΔθ = (1/2)Iωf2
(34.5)(107.442) = (0.5)(0.130)ωf2
3706.765 = 0.065ωf2
57027.156 = ωf2
238.8 = ω
 
  • #11
grzz said:
If you show your work help may be given.

But I just did o_O
 
  • #12
Looks like they want the speed in rev/s, not rads/sec.
 
  • #13
Doc Al said:
Looks like they want the speed in rev/s, not rads/sec.

Sooo...I don't convert angular displacement?
 
  • #14
riseofphoenix said:
Sooo...I don't convert angular displacement?
Convert your answer for ω from rad/s to rev/s.
 
  • #15
Doc Al said:
Convert your answer for ω from rad/s to rev/s.

τΔθ = (1/2)Iωf2
(34.5)(107.442) = (0.5)(0.130)ωf2
3706.765 = 0.065ωf2
57027.156 = ωf2
238.8 rad/s = ω

238.8/2π rev/s = ω
38 rev/s = ω

Awesome :eek:
Thanks!
 
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FAQ: Work done by a constant torque equation DOESN'T give me angular speed Help

1. What is the formula for work done by a constant torque?

The formula for work done by a constant torque is W = τΔθ, where W is the work done in joules, τ is the torque in newton-meters, and Δθ is the angular displacement in radians.

2. How does the work done affect angular speed?

The work done by a constant torque does not directly affect the angular speed. It is only one factor in determining the angular speed, along with the moment of inertia and the net torque.

3. Why doesn't the equation for work done give me the angular speed?

The work done equation only calculates the amount of work done, not the angular speed. To find the angular speed, you would need to use the equation ω = Δθ/Δt, where ω is the angular speed in radians per second, Δθ is the angular displacement, and Δt is the time taken.

4. Can I use the work done equation to find the angular velocity?

No, the work done equation does not directly give the angular velocity. To find the angular velocity, you can use the equation ω = Δθ/Δt or ω = v/r, where v is the linear velocity and r is the radius.

5. What other factors affect the angular speed besides work done?

Besides work done, the angular speed is also affected by the moment of inertia and the net torque. The moment of inertia is a measure of an object's resistance to change in its rotation, while the net torque is the sum of all the torques acting on an object.

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