A cockroach of mass m lies on the rim of a uniform disk of mass 4.00m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.260 rad/s. Then the cockroach walks halfway to the center of the disk.(a) What then is the angular velocity of the cockroach – disk system?(b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?(c) What accounts for the change in the kinetic energy?

Abumper car with a mass of 250 kg is traveling at a speed of 4 m/s. this bumper car collides and sticks to a second bumper car with a mass of 250 kg, which is initially at rest. what is the final speed of these two bumper cars after the collision, assuming they remain stuck together?

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

Which statement best explains why the overall charge on an atom is zero?