Calculating Torque for Spinning a 250g Plastic Disk on an Electric Motor in 4.6s

Nm=Inertia x 34013 rad/s2so now the equation would beTorque = Moment of Inertia x angular acceleration6.67x10-2Nm=Inertia x 34013 rad/s2Yes, correct. So what does that give for the moment of inertia?In summary, we are trying to determine the torque required for an electric motor to take a 250 g, 25-cm-diameter plastic disk from 0 to 1500 rpm in 4.6 s. Using the equation τ=Iα and information given about the disk's mass and dimensions, we can calculate the moment of inertia
  • #1
logan

Homework Statement


A 250 g , 25-cm-diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1500 rpm in 4.6 s ?

Homework Equations


ET=iα

The Attempt at a Solution


I just really don't know where to start
 
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  • #2
logan said:
ET=iα
Start by describing what the variables in that equation represent. E.g. "If a torque (variable name) acts on a mass with ..."
 
  • #3
Torque = Inertia x angular acceleration
 
  • #4
logan said:
Torque = Inertia x angular acceleration
Ok, so can you calculate the angular acceleration?
 
  • #5
to get angular acceleration you would have to do angular acceleration=Torque/Inertia and we don't know the torque
 
  • #6
logan said:
to get angular acceleration you would have to do angular acceleration=Torque/Inertia and we don't know the torque
No, you can calculate the angular acceleration from the information given.
logan said:
0 to 1500 rpm in 4.6 s
 
  • #7
so a=w/t
1500/4.6=326.08
 
  • #8
logan said:
so a=w/t
1500/4.6=326.08
Units?
 
  • #9
rad/s2
 
  • #10
logan said:
rad/s2
does rpm divided by seconds give rad/s2?
 
  • #11
so you have to convert the 1500 to rads?
so that would be 157
157/4.6=34013 rad
 
  • #12
logan said:
so you have to convert the 1500 to rads?
You have to convert from rpm to units involving radians, but not merely radians. Radians per ...?
logan said:
157/4.6=34013 rad
Eh?
 
  • #13
radians per second
 
  • #14
logan said:
radians per second
Ok. What about this part:
logan said:
157/4.6=34013 rad
?
Can you correct that now?
 
  • #15
so 157/4.6=34 radians per second?
 
  • #16
logan said:
so 157/4.6=34 radians per second?
You have 157 rad/s, and you are dividing by 4.6 s. What units result?
 
  • #17
Is it rad/s squared
 
  • #18
logan said:
Is it rad/s squared
Rad/s2, yes.

Next, can you calculate the moment of inertia of the disc?
 
  • #19
ok so that would be I=ta
4.6x34=156.4
 
  • #20
logan said:
I=ta
No, as you wrote the equation is τ=Iα, where τ is torque, I is moment of inertia and α is angular acceleration.
Do not confuse τ, torque, with t, time.

You have information about the disc. Use that find its moment of inertia.
 
  • #21
I=t/a
so t is 4.6 but how do you get the torque to solve for inertia

thanks for helping me out so much I am just so lost with this again thank you
 
  • #22
logan said:
I=t/a
so t is 4.6 but how do you get the torque to solve for inertia

thanks for helping me out so much I am just so lost with this again thank you
Go back and read the last sentence of post #20. How did I say you were to find the moment of inertia?

You don't seem to understand how equations work. In the equation τ=Iα, not only do you not know τ, you do not know any other way to find τ. So you must keep that equation in reserve for finding τ after you have already found I and α by other means. You cannot use the same equation twice, to find two different unknowns in it.

What information do you have about the disc itself?
 
  • #23
you know that the disk is 250 g and 25-cm-diameter
and it goes from 0 to 1500 rpm in 4.6 s
 
  • #24
logan said:
the disk is 250 g and 25-cm-diameter
That is the information you have about the disc itself, i.e. as an object. From that you can calculate its moment of inertia. Have you not been taught any equations for that?
 
  • #25
no my professor only went over Torque = Inertia x angular acceleration because he thinks by making the homework hard the test will be easy for us
 
  • #28
Perhaps worth pointing out the similarity between the equations for linear and rotational motion..

Linear...
Force = mass * acceleration

Rotation...
Torque = Moment of Inertia * angular acceleration

Both mass and moment of inertia depend on the stuff the object is made of and the dimensions.
Pretty much all the linear equations of motion can be adapted to rotation.
 
  • #29
so Ix would be .976
1/4(250)(.125)squared
 
  • #30
logan said:
so Ix would be .976
1/4(250)(.125)squared
Try to keep everything in SI units. You converted cm to m ok, but you also need to convert the g to kg.
The ¼ is for rotation of a disc about a diameter, Ix or Iy at the link I posted. For this problem you want rotation about the axis perpendicular to the disc, Iz.
 
  • #31
got it was 6.7x10^-2
thanks haruspex and cwatters
 
  • #32
Just for info I made it 6.45x10-2Nm
 
  • #33
CWatters said:
Just for info I made it 6.45x10-2Nm
I get 6.67x10-2.
 
  • #34
Oops yes found my mistake. Agree with your figure.
 

Related to Calculating Torque for Spinning a 250g Plastic Disk on an Electric Motor in 4.6s

1. How do you calculate the torque needed to spin a 250g plastic disk on an electric motor in 4.6 seconds?

To calculate the torque, you will need to know the rotational inertia of the disk, the angular velocity, and the time it takes to reach that velocity. The formula for torque is torque = rotational inertia x angular acceleration. You can find the rotational inertia by multiplying the mass of the disk by the square of its radius. The angular velocity can be calculated by dividing the total angle turned by the time it takes to turn that angle.

2. What is the rotational inertia of a 250g plastic disk?

The rotational inertia, also known as moment of inertia, depends on the shape and distribution of mass of the object. For a disk, the formula for rotational inertia is 1/2 x mass x radius^2. Therefore, for a 250g plastic disk, the rotational inertia will be 1/2 x 0.25kg x (radius)^2.

3. How do you determine the angular velocity of the disk?

The angular velocity can be calculated by dividing the total angle turned by the time it takes to turn that angle. For example, if the disk spins 180 degrees in 4.6 seconds, the angular velocity would be 180 degrees/4.6 seconds, or approximately 39.13 degrees per second.

4. Can you use a different unit of mass to calculate torque?

Yes, you can use any unit of mass as long as it is consistent throughout the calculation. For example, if you use kilograms for the mass of the disk, you will need to use kilograms for the rotational inertia as well.

5. How does the torque affect the spinning of the disk?

The torque is directly proportional to the angular acceleration of the disk. This means that the greater the torque, the faster the disk will spin. However, other factors such as friction and air resistance may also affect the spinning of the disk.

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