Determining torque required

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In summary, the angular momentum of a 2.8 kg uniform cylindrical grinding wheel with a radius of 18 cm rotating at 1500 rpm is 7.13 kgm^2/s. To determine the torque required to stop it in 7.0 s, you can use the formula T=Ia, where T is the torque, I is the moment of inertia, and a is the angular deceleration. Using the formula W(final)=W(initial)+a^t, you can calculate the angular deceleration to be 22.44 rad/s^2. Plugging this into the torque formula, you can determine that the torque required to stop the wheel in 7.0 s is -1
  • #1
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Problem 2) What is the angular momentum of a 2.8 kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?
b) How much torque is required to stop it in 7.0 s?


1500 rpm * 2pi rad = 9424.78 rad/m
(9424.78 rad/m) /60 s = 157.08 rad/s

I = 1/2mr2
I = 1/2(2.8 kg)(.18 m)2 = 0.04536 kgm2

L = Iw = (0.04536 kgm2)(157.08 rad/s) = 7.13 kgm2/s

I have determined the angular momentum, but I am unsure of how to determine the torque required to stop it in 7 s

How do you determine this with the torque formula and time involved? Any help?
 
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  • #2
The definition of torque is

[tex] \mathbf\tau = \frac{d\mathbf{\mathrm L}}{dt} [/tex]

If you want to change the angular momentum from your value to 0, then the average torque over 7 s most then be?
 
Last edited:
  • #3
t=(7.13 kgm^2/s)/7.0 s=1.02 kgm^2

Better?
 
  • #4
hmm...well you know the initial angular velocity ''157.08 rad/s''. I would say you need to calculate the angular deceleration of the spinning wheel from 157.08 r/s to 0 r/s in 7 secs using W(final)=W(initial)+a^t. I make the angular deceleration 22.44 rad s-2.

Then using the formula T=I x a...cha ching !
 
  • #5
w=w0+at
0=157.08+a(7)
-157.08=7a
a=-22.44 rad/s^2 since stopping

T=Ia
T=0.04536 kgm^2*-22.44
T=-1.02 m*N
 

1. What is torque and why is it important?

Torque is a measure of the force that causes an object to rotate around an axis. It is important because it helps determine the amount of force needed to move or rotate an object, and is crucial in understanding the performance and efficiency of machinery.

2. How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance between the point of force application and the axis of rotation. The formula is T = F x d, where T is torque, F is force, and d is the distance.

3. What factors affect the amount of torque required?

The amount of torque required is affected by several factors, including the weight and size of the object, the distance from the axis of rotation, the friction and drag forces, and the speed at which the object is rotating.

4. How do I determine the torque required for a specific task?

To determine the torque required for a specific task, you will need to know the weight and dimensions of the object, as well as the rotational speed and any additional forces acting on the object. You can then use the torque formula to calculate the required amount of force.

5. What are some practical examples of determining torque required?

Determining torque required is essential in many real-world applications, such as designing car engines, calculating the force needed to rotate a wind turbine, or determining the torque needed to lift heavy objects with a crane. It is also important in sports, such as determining the torque needed to swing a golf club or throw a javelin.

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