Angular Velocity of a hamster wheel

[lacar213]

Homework Statement

A hamster runs in its wheel for 4.5 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?

Homework Equations

angular velocity = ang displacement / time

The Attempt at a Solution

3 = angular displacement / 16200 seconds
angular displacement = 48600

I know this isn't the correct solution but I can't find an equation to help me solve this for m.

 

[physics girl phd]

The problem is looking for a linear length as if the hamster's wheel was running along the ground (not an angular displacement). You should be able to easily convert knowing a parameter of the wheel (the given radius).

 

[thomate1]

I would approach this problem by first converting the given information into SI units. The radius of the wheel is 0.068 meters and the angular velocity is 3.0 radians per second. Using the equation for angular velocity, we can calculate the total angular displacement of the wheel in one night:
angular velocity = angular displacement / time
3.0 rad/s = angular displacement / (4.5 hours x 3600 seconds/hour)
angular displacement = 3.0 rad/s x (4.5 hours x 3600 seconds/hour)
angular displacement = 48600 radians
Next, we can use the formula for arc length to calculate the distance the hamster runs in one night:
arc length = radius x angular displacement
arc length = 0.068 m x 48600 radians
arc length = 3304.8 meters
Therefore, the hamster runs approximately 3304.8 meters in one night. It is important to note that this calculation assumes that the hamster runs in a straight line without any interruptions or pauses. In reality, the hamster may run in a more erratic pattern and thus the actual distance may vary.