Calculating Net Torque of Uniform Disk

In summary, the net torque of a uniform disk can be calculated using the formula T = F*r*sin(θ), where T is the torque, F is the force, r is the distance from the center, and θ is the angle between the force and the radius. It can be negative, which means the direction of the torque is opposite to the direction of rotation. The mass of the disk does not directly affect the net torque, but can affect how the disk rotates. The shape of the disk does not affect the net torque. It can also be zero if the forces are balanced or their torques cancel out.
  • #1
copitlory8
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The circular blade on a radial arm saw is turning at 265 rad/s at the instant the motor is turned off. In 12.0 s the speed of the blade is reduced to 85 rad/s. Assume the blade to be a uniform solid disk of radius 0.140 m and mass 0.400 kg. Find the net torque applied to the blade.

Relevant Equations:
Torque net = 0
Torque= F(r)
F=ma
angular accel. = w2r

Attempt:
[tex]\sum[/tex]Torque=(.4)(265)2(.14)(.14) +(.4)(85)2(.14)(.14)
I known I need to sum the forces but I am unsure of what direction to use.
 
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  • #2
Answer:The net torque applied to the blade is zero. The angular acceleration of the blade must be in the opposite direction of the angular velocity, so the torque applied to reduce the angular velocity must be equal and opposite to the initial torque that caused the angular velocity. Therefore, the net torque is zero.
 

1. How do I calculate the net torque of a uniform disk?

To calculate the net torque of a uniform disk, you will need to know the force applied, the distance from the center of the disk to where the force is applied, and the radius of the disk. You can then use the formula T = F*r*sin(θ) to find the net torque, where T is the torque, F is the force, r is the distance from the center, and θ is the angle between the force and the radius.

2. Can the net torque of a uniform disk be negative?

Yes, the net torque of a uniform disk can be negative. This means that the direction of the torque is opposite to the direction of rotation. The magnitude of the torque will still be positive, but the direction will be different.

3. How does the mass of the disk affect the net torque?

The mass of the disk does not directly affect the net torque. The net torque is determined by the force and the distance from the center of the disk. However, the mass of the disk can affect how the disk rotates under the influence of the net torque. A heavier disk may rotate slower or require more torque to rotate at the same speed as a lighter disk.

4. Is the net torque of a uniform disk affected by the shape of the disk?

No, the net torque of a uniform disk is not affected by the shape of the disk. As long as the disk is uniform and the force is applied at a distance from the center, the net torque will be the same regardless of the shape of the disk.

5. Can the net torque of a uniform disk be zero?

Yes, the net torque of a uniform disk can be zero. This means that the forces acting on the disk are balanced and there is no rotation. This can occur if the forces are applied at equal distances on opposite sides of the center, or if multiple forces are applied at different distances but their torques cancel out.

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