Question

An object is traveling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
I think I've set my formula up right (v=Δ20/Δ1/3 radian), but I don't know what to do with the Δ thing. Once I know how to do that I should be able to like, actually figure it out.

Answer 1

Usually, Δ stands for a difference: if you have two quantities a₂ and a₁, their difference a₂-a₁ can be shortened as Δa.

This said, your formula is not set up correctly: the linear speed can be found with the formula:
v = ω·r
where r is the radius and ω is the angular frequency, which is given by:
ω = Δα / Δt
Substituting this into the one above, you find the correct formula:
v = (Δα / Δt) · r

The problem gives you directly Δα, which is 1/3 rad, because does not say at what angle the point started moving and at what angle it stopped.
Similarly, for the time you have Δt, which is 20 s.

Therefore, plugging in the numbers you get:
v = (Δα / Δt) · r = (1/3 ÷ 20) × 10 = 1/6 = 0.167 cm/s