Question

You throw a bowling ball down an alley with speed v_0v ​0 ​​ , and initially it slides without rolling. After a little while friction kicks in and the ball begins to roll. What is the speed of the bowling ball when it starts rolling without slipping?

Answer 1

Answer:

final speed after pure rolling is given as $R\omega = \frac{5}{7}v_0$

Explanation:

As we know that point of contact at ground is taken as reference then there is no external torque about this point on the ball

So we can use angular momentum conservation about this point

$L_i = L_f$

$L_i = mv_0R$

$L_f = \frac{7}{5}mR^2\omega$

so we have

$mv_0R = \frac{7}{5}mR^2\omega$

$R\omega = \frac{5}{7}v_0$

So final speed after pure rolling is given as $R\omega = \frac{5}{7}v_0$