Consider a bicycle wheel that initially is not rotating. a block of mass m is attached to the wheel via a string and is allowed to fall a distance h. assume that the wheel has a moment of inertia i about its rotation axis. now consider the case that the string tied to the block is wrapped around a smaller inside axle of the wheel of radius rb. find ωb, the angular speed of the wheel after the block has fallen a distance h, for this case.
express ωb in terms of m, g, h, rb, and i.
which of the following describes the relationship between ωa and ωb?
ωa> ωb
ωb> ωa
ωa=ωb

If an athlete runs once around a track, back to the starting line, her average velocity is zero. true or false?

Review multiple-concept example 7 in this chapter as an aid in solving this problem. in a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. in one instance, the radius of the circle is 0.626 m. at one point on this circle, the ball has an angular acceleration of 66.1 rad/s2 and an angular speed of 12.6 rad/s. (a) find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) determine the angle of the total acceleration relative to the radial direction.

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?