Angular displacement in radians

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Homework Help Overview

The problem involves calculating the angular displacement of a wheel given its radius and the force applied to a rope wound around it. The context includes concepts of angular motion and work done in rotational systems.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between revolutions and radians, with some noting the conversion from degrees to radians. Questions are raised about the initial steps needed to approach the problem, including how to calculate the work done in relation to torque and angular displacement.

Discussion Status

Participants are exploring foundational concepts related to angular displacement and the relationship between torque and work. Some have provided initial calculations and clarifications, but there is no explicit consensus on the next steps or a complete method yet.

Contextual Notes

There is a focus on understanding the definitions and relationships between the physical quantities involved, such as torque and angular displacement, without resolving the specific calculations required.

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Homework Statement


The radius of a wheel is 0.450 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 4.64 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope.


What is the angular displacement Δθ, in radians, of the wheel during 1.00 revolution?
Show that the numerical value of the work done is equal to the product τΔθ


Could someone please explain how to solve this
 
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What have you tried?

Where are you stuck?

If you wrap a rope around the wheel one time, how much rope does that take?
 
I do not know how to begin...
 
How many degrees correspond to one revolution?

How many radians is that equivalent to?
 
360 degress
2pie radian
 
That's a start.
 
ok got that, how do I Show that the numerical value of the work done is equal to the product τΔθ
 

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