A wheel 30 cm in diameter accelerates uniformly from 240 rpm to 380 rpm in 6.6 s .

Question

A wheel 30 cmcm in diameter accelerates uniformly from 240 rpmrpm to 380 rpmrpm in 6.6 ss .

How far will a point on the edge of the wheel have traveled in this time?

Express your answer to two significant figures and include the appropriate units.

Answer 1

You're given:

1. diameter = 30 cm (radius, r = 15 cm)
2. ω₀ = 240 rev/min (240 / 2π*60 rad/s)
3. convert this to rad/s using: 1 revolution = 2π and 1 minute = 60 seconds
4. ω_o = 2/π rad/s = 0.64 rad/s
5. ω_f = 380 rev/min (380 / 2π*60 rad/s)
6. ω_f = 3/π rad/s = 0.95 rad/s
7. Δt = 6.6s

You want to find distance, which in this case means find Δθ*r.

We need to remember (use) two angular kinematic equations:

1. ω_{f =} ω_i + α*t
2. ω_f² ₌ ω_i² + 2*α*θ

plugging in values for equation one tells us:

0.95 - 0.64 = 0.31 rad/s = α*6.6

1. α = 0.047 rad/s²

plugging into equation two we get:

θ = (ω_f² ₌ ω_i²) / 2*α = (0.95² - 0.64²) / 2*0.047 = 5.24

finally:

d = 5.24*15 = 79cm