Pring is an example of an object moving under the influence of a linear hooke's law force. the angular velocity of the mass on the spring, which gives us a sense of how often the motion repeats, is dependent on two parameters, spring constant (k) and mass (m). suppose that a mass of mass m has an angular velocity ω when attached to a spring with a spring constant k. determine the new angular velocity if the spring constant is increased by a factor

Amerry-go-round of radius r, shown in the figure, is rotating at constant angular speed. the friction in its bearings is so small that it can be ignored. a sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. the sandbag does not slip or roll upon contact with the merry-go-round. how would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest. a) m = 10kg, r = 0.25r b) m = 20kg, r = 0.25r c) m = 10kg, r = 0.50r d) m = 10kg, r = 1.0r e) m = 15kg, r = 0.75r f) m = 40kg, r = 0.25r