Torque, Angular Displacement, Work

In summary, the problem involves a wheel with a radius of 0.525m, a rope with a force of 5.45 N, and four questions to be answered. Part (a) asks for the amount of rope that unwinds while the wheel makes 1.00 revolution. Part (b) asks for the work done by the rope on the wheel during this time. Part (c) asks for the torque on the wheel due to the rope. Part (d) asks for the angular displacement of the wheel in radians during 1.00 revolution. Part (e) asks to show that the numerical value of the work done is equal to the product of torque and angular displacement.
  • #1
warrior2014
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0
Torque, Angular Displacement, Work!

Homework Statement


The radius of a wheel is 0.525m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.45 N, unwinding the rope and making the wheel spin counterclockwise about its central axis. Ignore the mass of the rope.
a) how much rope unwinds while the wheel makes 1.00 revolution?
b) how much work is done by the rope on the wheel during this time?
c) what is the torque on the wheel due to the rope?
d) what is the angular displacement Δθ, in radians, of the wheel during 1.00 revolution?
e) show that then numerical value of the work done is equal to the product τΔθ


Homework Equations



T= F*R

The Attempt at a Solution



I have no idea how to get this problem started. If anyone is able to help, please do so (I know there are a lot of parts to the question)! I'd really appreciate it :)
 
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  • #2


Are you saying you can't answer part (a) ?
 
  • #3


I figured out how to get (a), (b), (c) and (e) but unsure how to get (d). Could you please help me with that one?
 
  • #4


How did you get (e) without getting (d)?
 
  • #5


well the work done is going to be the same and since I knew that, I put the value in and it was correct
 
  • #6


The quick way to answer (d) is to realize how many radians correspond to one complete rotation of the wheel.
 
  • #7


how would you do part a?
 

1. What is torque?

Torque is a measure of the force that can cause an object to rotate about an axis. It is often described as a twisting or turning force.

2. How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied. The unit of torque is typically Newton-meters (Nm) in the metric system and foot-pounds (ft-lb) in the imperial system.

3. What is angular displacement?

Angular displacement is the change in an object's rotational position or orientation. It is usually measured in radians or degrees and can be positive or negative, depending on the direction of rotation.

4. How is angular displacement related to linear displacement?

Angular displacement is related to linear displacement through the radius of the circle or arc that the object is rotating along. The longer the radius, the greater the linear displacement for a given angular displacement.

5. What is work in terms of torque and angular displacement?

Work is the energy transferred to or from an object due to a force acting on it. In the case of torque and angular displacement, work is done when a force causes an object to rotate through a certain angle. The amount of work done is equal to the torque multiplied by the angular displacement.

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