Confused about torque vs. energy (Joules)

In summary, a solid disk with a diameter of 50cm and mass of 5kg is located in space by a bearing with a friction torque of 10Nm. A string connected to a weight is wrapped around the disk and allowed to fall, causing the disk to spin. The energy lost to friction can be calculated using the equation Work = torque (in Nm) * angular displacement (in Radians). The total energy lost due to friction is not the same as the frictional torque and there is a relation between work and torque and the total angle turned.
  • #1
johnschmidt
12
0

Homework Statement



Solid disk, 50cm in diameter, with a mass of 5kg. Disk is located in space by a bearing. The friction torque of the bearing is 10Nm. A string is wrapped around the disk and connected to a weight. The weight is allowed to fall and spin the disk. How much energy is lost to friction?

Homework Equations



1 Joule = 1Nm

The Attempt at a Solution



Since the friction torque is 10Nm, the energy lost to friction is 10J (same as 10Nm). Is this right? I'm confused by torque having the same units as Joules...
 
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  • #2
Do you remember the equation...

work = force (N) * distance (m)

Well the equivalent for rotation is...

Work = torque (in Nm) * angular displacement (in Radians)
 
  • #3
Even worse for you, the total energy lost due to friction is not the same as the frictional torque. There is a relation between work and the torque and the total angle turned. It is similar to the work resulting from a force translating a certain distance.
 

1. What is the difference between torque and energy?

Torque and energy are two different physical quantities that are often confused with each other. Torque is a measure of the force that causes an object to rotate, while energy is the ability of an object to do work or create motion. In simpler terms, torque is a twisting force, while energy is the ability to cause change.

2. How are torque and energy related?

Torque and energy are related through the concept of work. Work is defined as the product of force and displacement, and torque is a type of force. Therefore, when a torque is applied to an object and it rotates, work is being done and energy is being transferred.

3. Can torque and energy be measured in the same units?

No, torque and energy are measured in different units. Torque is typically measured in units of Newton-meters (Nm) or foot-pounds (ft-lb), while energy is measured in units of Joules (J). This is because torque is a measure of force and distance, while energy is a measure of force and time.

4. How does understanding torque and energy help in practical applications?

Understanding the difference between torque and energy is important in many practical applications, such as engineering, mechanics, and physics. For example, in designing a machine, it is crucial to consider both the torque required to rotate the parts and the energy needed to power the machine. In physics, understanding torque and energy can help explain rotational motion and the conservation of energy.

5. Is torque or energy more important?

Both torque and energy play important roles in different contexts, so it is difficult to say which is more important. In terms of rotational motion, torque is necessary for an object to rotate, while energy is necessary for the object to continue rotating. In terms of practical applications, both torque and energy are equally important and must be considered together for proper functioning of machines and systems.

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