A disk with a mass of "m" kg and radius of "r" meters (l =1/2mr^2) rolls without slipping at "v" m/s. 1. What is its total kinetic energy (in terms of m,r, and v)?

An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.9 rad, b = 0.75 rad/s2 and c = 0.025 rad/s3.Randomized Variables a = 1.9 radb = 0.75 rad/s2c = 0.025 rad/s3 1) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1?  2)  Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values.  3) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?

A figure skater performs a twisting jump. She rotates around her longitudinal axis 2 times in 0.65 s.  What was her average angular velocity in radians/second? A   720rad/s  B   19.3rad/s C   4? rad/s D   9.67 rad/s E   1107 rad/s

A merry-go-round is a common piece of playground equipment. A 5 m diameter (that's diameter) merry-go-round rotates frictionlessly. It has a mass of 166 kg and is spinning at 22 rpm (that's revolutions/minute... you will want to convert to radians/sec). John runs tangent to the merry-go-round at 2.5 m/s in the same direction that it is turning. John's mass is 27 kg. He then jumps onto the MGR and sits halfway between the outer edge and the center.   (A)What is the initial angular momentum, LJ, of John? (B)What is the total initial angular momentum of the system? (C)Use Conservation of Angular Momentum to find the final angular speed of the merry-go-round?

A ship's wheel can be approximated as an annular cylinder (different from a ring) of mass 6.7 kilograms, inner radius 25 centimeters, and outer radius 32 centimeters; and eight spokes of mass 0.50 kilograms and length 49 centimeters.   a. What is the moment of inertia? Include units in your answer. More information. b. Disagreeing over which way to go, the captain and the helmsman try to turn the wheel in opposite directions. The captain applies a force of 311 newtons at the inner radius, while the helmsman applies a force of 287 newtons at the outer radius. What is the magnitude of the angular acceleration of the wheel? Include units in your answer.

4

A solid cylindrical disk whose mass is 1.4 kg and radius is 8.5 cm, rolls across a horizontal table at a speed of 15 cm/s. What is the instantaneous velocity of the top of the rolling cylinder? What is the angular speed of the rolling disk? What is the kinetic energy of the rolling disk?

A 16 gm DVD disc with a diameter of 120mm rotates with an angular speed of 115 rad/second. What is the Kinetic Energy of the spinning DVD?

A Ferris wheel on a California pier is 27 m high and rotates once every 32 seconds. When the wheel starts turning, you are at the very top.a. What is your angular position 75 seconds after the wheel starts turning, measured counterclockwise from the top?Express your answer as an angle between 0° and 360°.b. What is your speed ν?

A merry-go-round is a common piece of playground equipment. A 5 m diameter (that's diameter) merry-go-round rotates frictionlessly. It has a mass of 166 kg and is spinning at 22 rpm (that's revolutions/minute... you will want to convert to radians/sec). John runs tangent to the merry-go-round at 2.5 m/s in the same direction that it is turning. John's mass is 27 kg. He then jumps onto the MGR and sits halfway between the outer edge and the center. A)What is the rotational inertia of the merry-go-round (consider it a disk)? B)What is the initial rotational inertia of John (consider him a point mass). C)What is the initial angular momentum, Lmgr, of the merry-go-round? (D)What is the initial angular momentum, LJ, of John? (E)What is the total initial angular momentum of the system? (F)Use Conservation of Angular Momentum to find the final angular speed of the merry-go-round?