How Do You Correctly Cancel Angular Momentum in Physics Problems?

[pbnj]

Homework Statement

A ball with mass $m$ and diameter $D$ is thrown with speed $v$ at an angle $\theta$ with the horizontal from a height $h_i$. How much spin (in rad/s) must the thrower impart on the ball so that at its maximum height, it has no angular momentum with respect to a point on the ground directly beneath the ball?

Relevant Equations

$v_f^2 = v_i^2 + 2a\Delta h$
$L = I\omega$
$L = \vec r \times \vec p$

First, we calculate the maximum height using the first equation, noting that at maximum height, the velocity is purely horizontal with speed $v\cos\theta$, and with initial vertical speed $v\sin\theta$:

$$
\begin{align}
v_f^2 &= v_i^2 - 2g(h_f - h_i) \\
0 &= (v\sin\theta)^2 - 2g(h_f - h_i) \\
h_f &= \frac{(v\sin\theta)^2}{2g} + h_i
\end{align}
$$

The angular momentum from translation is given by $L_t = \vec r \times \vec p = h_f\hat j \times mv\cos\theta\hat i = -h_fmv\cos\theta\hat k$. The moment of inertia of a sphere is $I = \frac 2 5 mR^2$ where $R = \frac D 2$, and its angular momentum due to spin is $L_s = I\omega$.

We need these to cancel, so

$$
\begin{align}
L_t + L_s &= 0 \\
-h_fmv\cos\theta + \frac 2 5 mR^2\omega &= 0 \\
\omega &= \frac{h_fmv\cos\theta}{\frac 2 5 mR^2} \\
&= \frac{5h_fv\cos\theta}{2R^2}
\end{align}
$$

The problem uses $m = 625g$, $D = 22.9cm$, $\theta = 45^\circ$, $v=5m/s$ and $h_i = 1.5m$. Using these values I get a spin of about $1440.82$, in rad/s.

 

[kuruman]

Your answer agrees with mine.

 

[haruspex]

Using these values I get a spin of about 1440.82, in rad/s.

Have you a reason to doubt it?

 

[pbnj]

Have you a reason to doubt it?

It's for a Coursera course, and it tells me it's incorrect. I've tried incrementing/decrementing my answer by 5 a few times, I tried using 2 sigfigs for everything, I tried assuming "diameter" meant "radius," but no luck. On the discussion forum there are no questions about this particular answer (the course is 3 years old, and it doesn't seem like new posts get replies). If my approach is correct and my calculations are correct, I can only assume something in the backend changed in the 3 years between then and now.