How Do You Calculate the Force to Slow a Spinning Disc to a Stop?

In summary, the problem involves finding the force required to slow a spinning disc with a known moment of inertia and angular velocity to a stop in a given time. The solution involves using the equations for torque and deceleration, and taking into account the added mass of a lump of clay on the disc. The final answer is 0.427N.
  • #1
bobbles22
17
0

Homework Statement


I need a quick sanity check here please. (Sorry, my alphas keep coming out as power signs, they're not!).

To find the force to slow a spinning disc with known moment of inertia (0.0004kgm2) and known angular velocity (120pi rad/s) to a stop in 6s.

Here, the deceleration ([tex]\alpha[/tex]) is 120pi/6=20 rad/s2. The radius of the disc is 6cm=0.06m


Homework Equations



Torque = rf (r=radius, f=force)

Also, torque=I[tex]\alpha[/tex]

And [tex]\alpha[/tex]=w/t where w=angular velocity (120pi) and t= the time to slow=6s.

This gives [tex]\alpha[/tex] to be 20pi rad/s2.


The Attempt at a Solution



Setting rf=I[tex]\alpha[/tex]

0.06f=0.0004 x 20pi

From this, the force is given to be 0.42N.

Could someone just check if this is right. I think I've done it ok, but its been some time. It kind of looks right to me, but part of me is thinking I've missed something. It seems too easy. Any help greatly appreciated.
 
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  • #2
Looks good to me. (Assuming the force is applied tangentially.)

To get your latex to align with the rest of a sentence, use the inline tag (itex) instead of the regular tag (tex): [itex]\alpha[/itex] versus [tex]\alpha[/tex].
 
  • #3
Opps. I forgot to add the lump of 5g of putty 4cm from the centre of the disc. This makes the total moment of inertia (0.004+0.005x0.042.

Therefore 0.06f=0.000408x20pi

so f=0.427N

But, thank you if you think that is right :wink:
 
  • #4
How did the lump of clay get there? If the clay and disk start out rotating together at the given speed, then your answer is fine.
 
  • #5
Yes, the clay was added as an earlier part of the question, hence I originally only had the moment of inertia of the disc (0.0004) and then changed it for the moment of inertia of both the disc and clay (0.004 + 0.005 x 0.0016 where the distance of the clay from the centre is 4cm, and its mass 5g. As it is a single particle on the disc, its own moment of inertia I worked using mr2, unlike 1/2 mr2 for the disc as the disc is a solid rotating object whilst the particle inscribes a hollow track).
 

Related to How Do You Calculate the Force to Slow a Spinning Disc to a Stop?

1. What causes a spinning disc to slow down?

The main cause of a spinning disc slowing down is friction. When the disc is spinning, the surface it is on or any air particles it comes in contact with create resistance, which in turn causes the disc to slow down.

2. How can you slow a spinning disc to a stop?

To slow a spinning disc to a stop, you can apply a braking force. This force counters the motion of the disc and slows it down until it eventually stops. Another way is to reduce the friction between the disc and the surface it is on, such as by placing it on a smooth surface or lubricating the surface.

3. Does the speed of the spinning disc affect how quickly it slows down?

Yes, the speed of the spinning disc does affect how quickly it slows down. The faster the disc is spinning, the more friction it will encounter and the quicker it will slow down. This is because a higher speed means the disc is making more contact with its surroundings, creating more resistance and friction.

4. Can the material of the disc affect how quickly it slows down?

Yes, the material of the disc can affect how quickly it slows down. Different materials have different levels of friction and resistance, which can impact how quickly the disc slows down. For example, a disc made of a smooth metal will experience less friction than a disc made of a rougher material like wood.

5. Is it possible to completely stop a spinning disc?

Yes, it is possible to completely stop a spinning disc. By applying a strong enough braking force and reducing the friction, the disc will eventually come to a complete stop. However, this may take some time depending on the speed and material of the disc.

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