Question

You are enjoying some time at your towns annual summer carnival. You first decide to stop and play a game. In this game, a large solid wheel with a mass of 23 kg and a radius of 0.97 m is set up in a horizontal plane (assume the shape of the wheel is a solid cylinder). The person running the game spins the wheel and players stand above the wheel and need to drop beam bags (m = 1.2 kg) onto the heel trying to hit specific spots in order to win on a prize. The wheel is spinning at an angular velocity of 1.2 revolutions per second when you drop your first bean bag. The bean bag lands on the red spot. If you drop your bean bag onto the wheel as a result the angular velocity of the wheel slows down by 8%, how far from the center of the wheel is the red spot located?

Answer 1

To solve this we are going to use the angular momentum, to calculate de distance of the red spot. The momentum is not going to change, so the initial total momentum has to be the same as the final total momentum

`\begin{gathered} \sum_{n\mathop{=}0}^(\infty)L=m\cdot r^2\cdot w=23kg\cdot(0.97m)^2\cdot1.2s^(-1)=25.97kg\cdot m^2/s,\text{ initial momentum} \\ \sum_{n\mathop{=}0}^(\infty)L=L1+L2=m1\cdot r1^2\cdot w1+m2\cdot r2^2\cdot w2,\text{ final momentum} \end{gathered}`

Both momentums are the same, so now we can equal both expressions