Calculating Torque & Power of a Rotating Disk

In summary, the problem involves calculating the torque and power for a disk of radius 0.5 m subjected to a force of 50 N and rotating at an angular velocity of 100 rad/s. The torque is found to be 25 Nm and the power is calculated to be 2500 Nm/s, which is the answer given in the solutions book. The use of radians in units can sometimes be confusing and may disappear when mixed with other units. Further research may be needed to fully understand this concept.
  • #1
kostantina
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Homework Statement



So I am calculating torque and power for a disk of radius 0.5 m that is subjected to a force of 50 N at its periphery and is rotating at angular velocity of 100 rad/s. Find torque and power.[/B]

Homework Equations



Torque= radius x Force = 0.5m *50N = 25Nm

Power= dW/dt= F*w(omega)= 25Nm * 100 rad/sec ... WHy the solutions book has an answer 2500 Nm/s. Why did they ignore the radians. I was thinking to convert the radians into meters or something like that. What am I not understanding here?
 
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  • #2
Radians are a sort of "unitless" unit. They arise out of ratios of like units, such as the ratio of the circumference of a circle to its radius (with suitable unitless constants involved). So when they get mixed up with "real" units they have a tendency to disappear. So, rad*m = m, rad*kg = kg, and so on.
 
  • #3
Thank you for the response. It makes sense now. Will do further research on this to make sure I understand.
 

Related to Calculating Torque & Power of a Rotating Disk

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

The torque of a rotating disk can be calculated by multiplying the force applied to the disk by the distance from the point of rotation to where the force is applied. The formula for torque is T = F x r, where T is torque, F is force, and r is the distance from the point of rotation to where the force is applied.

2. What units are used to measure torque?

Torque is typically measured in Newton-meters (Nm) in the SI (International System of Units) measurement system. However, it can also be measured in pound-feet (lb-ft) in the English measurement system.

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

The mass of the rotating disk does not directly affect the torque. However, the mass distribution of the disk can affect the torque by changing the distance from the point of rotation to where the force is applied. A heavier disk with more mass concentrated at the outer edge will have a greater torque compared to a lighter disk with the same amount of mass distributed evenly.

4. Can torque and power be calculated at any point on the rotating disk?

Yes, torque and power can be calculated at any point on the rotating disk as long as the force and distance from the point of rotation are known. However, it is important to note that the torque and power may vary at different points on the disk due to changes in distance and force.

5. How do I calculate the power of a rotating disk?

The power of a rotating disk can be calculated by multiplying the torque by the angular velocity (ω) of the disk. The formula for power is P = T x ω, where P is power, T is torque, and ω is angular velocity measured in radians per second (rad/s).

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