An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall eve when the floor is removed. The coefficient of static friction between the person and the wall is u, = 0.3 and the radius of the drum is R= 2m. (a) Find wmin, the minimum angular speed at which the drum should rotate such that the person is held up even if the floor is removed. (hint: when th floor is removed, the person is held up by the static frictional force). (b) Find the linear speed of the person when the drum is rotating at the minimum angular speed you found in (a) (c) Suppose that the drum started from rest and reached the speed you found in (a) in 120 seconds. During this time the drum had constant angular acceleration. Find the number of rotations made by the person within this time.

A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is 13.5kgm2 and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is 3.4kgm2 and she has 2.0 s to do the flips in the air?

Suppose a piece of dust has fallen on a CD. If the spin rate of the CD is 500 rpm, and the piece of dust is 4.3 cm from the center, what is the total distance traveled by the dust in 3 minutes? (Ignore accelerations due to getting the CD rotating.)

A bowling ball of radius 8.5 cm is tossed onto a bowling lane with speed 9.0 m/s. The direction of the toss is to the left, as viewed by the observer, so the bowing ball starts to rotate counterclockwise when in contact with the floor. The coefficient of kinetic friction on the lane is 0.3. (a) What is the time required for the ball to come to the point where It is no slipping? What is the distance d to the point where the ball is rolling without slipping?

In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m from the center. He then mountsthe tire in a vertical plane and notes that the radius vector to thespot is at an angle of 35.0 with the horizontal. Starting from rest,the tire is spun rapidly with a constant angular acceleration of 3.00 rad/s2. a. What is the angular speed of the wheel after 4.00 s? b. What is the tangential speed of the spot after 4.00 s? c. What is the magnitude of the total accleration of the spot after 4.00 s?" d. What is the angular position of the spot after 4.00 s?

A space station is coast me ted in the shape of a hollow ring of mass 5.00 104 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r = 100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (Sec Fig. P11.29.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring, (a) What angular momentum does the space station acquirer (b) For what time interval must the rockets be fired if each exerts a thrust of 125 N?

A diver off the high board imparts an initial rotation with his body fully extended before going into a tuck and executing three back somersaults before hitting the water. If his moment of inertia before the tuck is 16.9kgm2 and after the tuck during the somersaults is 4.2kgm2 , what rotation rate must he impart to his body directly off the board and before the tuck if he takes 1.4 s to execute the somersaults before hitting the water?

Suppose a child walks from the outer edge of a rotating merry-go-round to the inside. Does the angular velocity of the merry-go-round increase, decrease, or remain the same? Explain your answer. Assume the merry-go-round is spinning without friction.

Jupiter rotates about its axis once every 9 hours 55 minutes. a. What is Jupiter's angular speed of rotation? b. What is the effect of this rapid rotation on the shape of theplanet?

A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.