Question

After 14.6 s, a spinning roulette wheel has slowed down to an angular velocity of 1.22 rad/s. During this time, the wheel has an angular acceleration of -4.51 rad/s2. Determine the angular displacement of the wheel.

I did
w0= wf + (4.51)(14.6) = 1.22+45.1

46.32(14.6) - (1/2)(4.51)(14.6)(14.6) = 159

Did I do this correctly?

Answer 1

ω=ωₒ - ε•t,
ωₒ= ω+ ε•t =1.22+4.51•14.6 =67.1 rad/s.
φ = ωₒ•t - ε•t²/2 =67.1•14.6 – 4.51(14.6)²/2 =1468 rad