Solving for Distance of a Rotating Wheel

[julz3216]

Homework Statement

A wheel 31.8 cm in diameter accelerates uniformly from 242 rpm to 380 rpm in 7.66 s. How far will a point on the edge of the wheel have traveled in this time?

Homework Equations

angle = initial angle +angular velocity(t) + .5(angular acceleration)(t)

w=initial angular velocity +angular acceleration (t)

and s=R*angle

The Attempt at a Solution

i tried plugging into the equations but i really don't know what to do

 

[LowlyPion]

angle = initial angle +angular velocity(t) + .5(angular acceleration)(t)

Not quite.

θ = θ_o + ω*t + 1/2*α*t²

Where θ is in radians.

And there are 2π radians in a revolution.

First convert your ω's to radians/sec from rpm and figure α and then you can figure your θ.

To find distance ... x = θ *r

 

[julz3216]

I converted to rad/sec so its 25.34 and 39.79
I found a = (39.79-25.32)/7.66 =1.886
then I used θ = θo + ω*t + 1/2*α*t2
and did θ = 0 + 25.34*7.66 + 1/2*1.886*7.66 = 249.435

So i got x=θR = 249.435(15.9) = 3966.01

But this is wrong, is there something else I need to convert or calculate?

 

[LowlyPion]

But this is wrong, is there something else I need to convert or calculate?

Without doing any other math I would note the diameter is .318m.

Always, always stay in SI units wherever possible.

 

[julz3216]

Oh ok, that's what I did wrong. I got it. Thank you!