Distance, angular velocity

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1. Feb 20, 2016

katie beisel

1. The problem statement, all variables and given/known
A hamster runs in its wheel for 2.7 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?

2. Relevant equations
w= delta theta/change in time

3. The attempt at a solution
6.8 cm x .001m/1 cm = .0068 m
2.7 hrs x 3600s/1 hr = 9720 s
c = 2pi(.0068m) = .0427 m
3.0 rad/s = delta theta / 9720 s
=29160
the correct answer is 2.0 x 10^3

2. Feb 20, 2016

Staff: Mentor

Check your centimeter to meter conversion? Remember there are 100 cm per meter right.

3. Feb 20, 2016

katie beisel

oh whoops yeah
then its .068 m
im still not sure where to go from there

4. Feb 21, 2016

SteamKing

Staff Emeritus
You've converted the radius of the wheel from centimeters to meters.

You know that the hamster spins the wheel at 3 rad/s. How fast is this for a wheel with a radius of 0.068 m?

5. Feb 21, 2016

katie beisel

so
i got that one rotation takes .157 seconds but i still dont know where to go from there

6. Feb 21, 2016

SteamKing

Staff Emeritus
You still haven't applied the definition of what a radian is to this problem.