Consider an object on a rotating disk a distance ? from its center, held in place on the disk by static friction. Which of the following statements is true concerning this object? Multiple statements can be true.

A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 2 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 120 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)? Please write out steps, not type-I have dyslexia

A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?

An automobile traveling 110 km/h has tires of 69.0 cm diameter. (a) What is the angular speed of the tires about their axles? (b) If the car is brought to a stop uniformly in 21.0 complete turns of the tires, what is the magnitude of the angular acceleration of the wheels? (c) How far does the car move during the braking? (Note: automobile moves without sliding) (a) Number i Units (b) Number i Units (c) Number i Units

NASA physicians need to know whether the contents of astronauts' skulls (brain, eyes, eardrums, etc.) move so much during rotational maneuvers that injury might be caused. If you are an astronaut in a spinning spacecraft and have an initial angular displacement of 3.14 radians, an initial angular velocity of 3.683 radians per second, and an angular acceleration of 0.02 radians per second squared, what distance will your eyes have traveled around the center of your skull after 26.83 seconds?

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 8.70 rev/s; 35.0 revolutions later, its angular speed is 20.0 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 35.0 revolutions, (c) the time required to reach the 8.70 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 8.70 rev/s angular speed. Unit (a) Number (b) Number Unit (c) Number Unit (d) Number Unit

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10.0 rev/s; 65.0 revolutions later, its angular speed is 16.0 rev/s. Calculate (a) the angular acceleration (rev/s?), (b) the time required to complete the 65.0 revolutions, (c) the time required to reach the 10.0 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 10.0 rev/s angular speed. (a) Number i Unit (b) Number i Unit (c) Number i Unit (d) Number i Unit>>>

Consider the 15.0 kg motorcycle wheel shown in the figure. Assume it to be approximately an annular ring with an inner radius of R1 = 0.280 m and an outer radius of R2 = 0.480 m. The motorcycle is on its center stand, so that the wheel can spin freely. a)If the drive chain exerts a force of 2450 N at a radius of 5.00 cm, what is the angular acceleration of the wheel in rad/s2? _____rad/s2 (b)What is the tangential acceleration, in m/s2, of a point on the outer edge of the tire? ______m/s2 (c)How long in seconds, starting from rest, does it take to reach an angular velocity of 80.0 rad/s? _______s

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 6.60 rev/s; 45.0 revolutions later, its angular speed is 24.0 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 45.0 revolutions, (c) the time required to reach the 6.60 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 6.60 rev/s angular speed. (a) Number Unit (b) Number i Unit (c) Number i Unit (d) Number Unit

A playground merry-go-round is essentially a uniform disk that rotates about the vertical axis through its centre. Suppose the disk has a radius of 'r' m. Which way is more effective to turn the disk?(1) Applying a tangential force 'F' to the disk.(2) Applying a force 'F' through the centre of rotation.Choose answer as (1) or (2) and explain.(3) Is there still a more effective way to turn the disk? If yes, explain.