An amusement park ride operates as follows: riders enter the cylindrical structure when it is stationary with the floor at the point marked "a". They then stand against the wall as the cylinder then begins to rotate. When it is up to speed, the floor is lowered to the position marked "b", leaving the riders "suspended" against the wall high above the floor: r 1.5m us 0.50 mb 73 kg = Determine the period of rotation necessary to keep the riders from sliding down the wall when the floor is lowered Show all your work! Include a general diagram, knowns/unknowns, free body diagram, net force equations, and a symbolic solution! When you are done check that you get the following answer: T_max = 1.74 seconds

You are swinging a sling shot, which is basically a string tied to a rock, vertically as shown. After you get it going fairly fast, you hold your hand stationary so it swings around in a perfect circle. The rock slows down as it gets higher and speeds up as it comes back down. One simple model for how this would work is that the tangential component of the rock's velocity isvt(t)=v0-(v0/4)sin((2pi/T)t)  where v0 is the rock's speed at t=0s and T is the time it takes the rock to go all the way around the circle. Call L the length of the string. 1. What is the total acceleration of the rock? 2. What is the angular Acceleration?

Suppose that humans have created a colony outside of our solar system on a planet called Wfirst21. Wfirst21 has a mass of 1.45×1025 kg and a day that lasts 24.1 h (which defines the rotational period of the planet). The colony is located on the planet's equator. The colonists set up a communications satellite which orbits Wfirst21. The satellite has a circular orbit that keeps it positioned directly above the colony. Calculate the radius ?r of the satellite's orbit in kilometers.

A 50.0 kg child stands at the rim of a merry-go-round of radius 1.70 m, rotating with an angular speed of 2.95 rad/s. (a) What is the child's centripetal acceleration? m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? N(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?

Artificial gravity is a must for any space station if humans are to live there for extended length of time. An effective way to create artificial gravity is using a rotating enclosed cylinder. Humans walk on the inside of the outer edge of the cylinder, which has a diameter of D=3450m that is large enough such that its curvature is not readily noticeable to the inhabitants. Once the space station is rotating at the necessary angular speed w to create an artificial gravity of 1g, how many minutes would it take the space station to make one revolution?

NASA scientists suggest using rotating cylindrical craft to recreate gravity while in a weightless environment. Consider such a craft that has a diameter of d = 124 m. What is the speed v, in meters per second, the craft must rotate at its outer edge to recreate the force of gravity on earth g.  At what rate, in revolutions per minute, is the station rotating?

A planet orbits a star, in a year of length 2.29 x 10’ s, in a nearly circular orbit of radius 3.81 x 1011 m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration. (a) Number i Units (b) Number i Units (c) Number i Units >

A ball is tied to a string and whirled in a horizontal circle at a constant 4 revolutions per second. Categorize the following according to whether they are 0 in value, constant in value, or change: v: linear speed (scalar) v. linear velocity (vector) a: radial (centripetal) acceleration (scalar) a: radial (centripetal) acceleration (vector) u angular speed (scalar) w angular velocity (vector) a angular acceleration (scalar) a angular acceleration (vector constant and non-zero constant and 0 non-constant radial acceleration (scalar) radial acceleration (vector) angular velocity (vector) linear velocity angular acceleration (vector) linear speed angular speed angular acceleration (scalar)