You throw a small toy ball that is covered with suction cups at the center of your glass patio door. When it hits it sticks to the glass, and because the door was not latched, it causes the door to swing open with an angular velocity of 0.19 rad/s. If the ball has a mass of 120 g and the patio door can be treated as a uniform box that is 2.3 m high, 1.0 m wide, and 0.030 m thick with a mass of 7.5 kg what speed did you throw the ball at

Explanation:

moment of inertia of the door M = 1 /3 m ( l² + b² + d² )

= 1 / 3 x 7.5 x ( 2.3² + 1² + .03² )

= 1 / 3 x 7.5 x 6.2909

I = 15.7272.

moment of inertia of the door + small toy

15.7272 + .12 x .5²

= 15.7272 + .03

= 15.7572

Applying conservation of angular momentum law

mvr = M ω

m is mass of the toy thrown with velocity v at distance r from the axis , M is moment of inertia of door + toy and ω is angular velocity ith which door opens.

.12 x v x .5 =  15.7572 x .19

v = 49.89 m /s .

wavelength divides in half and speed stays the same.