I'm trying to derive equations for $\theta(t)$ and $r(t)$ when modelling a backspin shot in pool.
I am of the understanding that the rotational deceleration is $\ddot \theta(t)=\dfrac{m\mu_sgR}{I}$ where $\mu_s$ is the coefficient of sliding friction.
However, the values that I have for the real world gives me a crazy deceleration.
- mass of whiteball $96$g = $0.096$kg
- radius of whiteball $\frac{15}{16}$in = $2.38$cm = $0.0238$m
- coefficient of sliding resistance = $0.3$
- $g = 9.8$m/s²
- Moment of inertia $I$ = $\frac{2}{5}mR^2$ = $0.0000218$ kg m²
Subbing all of this in gives $\ddot \theta(t)=\dfrac{0.096 \times 0.3 \times 9.8 \times 0.0238}{0.0000218}\approx 300$
Why am I getting an angular acceleration of $300$ rad / second²? A value online suggests that it should be between $5 - 15$ rad / second².