Can someone explain/show how to set this problem up

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Homework Help Overview

The problem involves a hamster running in a wheel, focusing on calculating the distance traveled based on the wheel's radius and the hamster's angular velocity over a specified time period.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss converting angular velocity into turns and consider how to relate the radius of the wheel to the distance traveled. Questions arise about the appropriate equations and unit conversions needed to find the distance for one complete turn.

Discussion Status

There is an ongoing exploration of the relationships between angular velocity, time, and distance. Some participants are questioning the units and the necessary calculations to determine the circumference of the wheel, while others are attempting to clarify the setup of the problem.

Contextual Notes

Participants are working within the constraints of the problem as presented, with a focus on understanding the relationships between the given quantities without providing a complete solution.

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A hamster runs in its wheel for 3.1 hours every night. If the wheel has a 6.8 cm radius and its average angular velocity is 3.0 radians per second, how far does the hamster run in one night?
 
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I would convert that 3 radians into a number of turns. I think a full turn is 2*pi radians, so it is about half a turn per second. How far does the hamster go in a turn?
 
So, 3.0/2pi=.4774648

3.1 hours * 3600secs=11160 Secs

Now what to do with the radius, and what equation to use

thanks
 
Not quite, look at your units. He runs at 3rads/s and the entire circle is 2pi rads. You want to find the time it takes to go through the entire circle. Once you find that you need to find how far one complete turn is. The hamster travels the circumference of the circle each revolution. How far is that?
 

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