Physics formula?

Question

what formula would I use to solve this? I forgot my book at school...

In 1987, a giant hanging basket of flowers with a mass of 4000kg was constructed. The radius of the basket was 3 m. Suppose this basket was placed on the ground and a spectator ran around it. At first the spectator's angular speed was 0.82 rad/s, but he steadily decreased his speed to 0.36 rad/s by the time he had traveled 20 m around the basket. Find the spectator's angular acceleration.

there's more questions but they're all the same section so they're probably the same formula.

Answer 1

Angular acceleration = change in angular speed / time
or: α = Δω / t
Thus, you don't need mass.

In this case, since you don't have time given, you need to use Torricelli's equation converted to angular velocities:
ωf^2 = ωo^2 + 2αd

ωo = original angular velocity = .82 rad/sec
ωf = final angular velocity = .36 rad/sec
d = 20m (need to convert to radians)

Since the radius of the basket is 3m, the circumfrence = πd = 2rad
1 rad thus = 3π m
20 m * 1 rad/3π m = 2.122 rad

Now, plug all this in:
ωf^2 = ωo^2 + 2αd
(.36 rad/s)^2 = (.82 rad/s)^2 + 2α(2.122)
0.1296 = 0.6724 + 4.244α
4.244α = -0.5428
α = -0.12790 rad/s^2 (solution!)

Check:
d = ωot + 1/2αt^2
2.122 rad = .82 rad/s * t + 1/2 (-0.12790) rad/s^2 * t^2
0 = -.06395 t^2 + .82t - 2.122

Use quadratic formula:
t = (-b +/- (b^2 - 4ac)^1/2)/2a
t = (-.82 +/- (0.6724 - 0.5428076)^1/2) / -0.1279
t = (-.82 +/- 0.3600)/-0.1279
t = 3.597 and 9.226

Only 3.597 makes sense in this context - 9.226 sec would be if the angular velocity becomes negative (spectator reverses course).

Now, plug t into the basic equation for angular acceleration:
α = Δω / t
-0.12790 = (.36 - .82) / 3.597
-0.12790 = -0.12788 (check!)

Answer 2

attempt writing each and every formulation 15 situations. this could help with the memmorization. additionally, relatively some physics formulae could nicely be derived, so with slightly calculus, you purely could undergo in innovations some equations.