Adisk, with a radius of 0.30 m, is to be rotated like a merry-go-round through 800 rad, starting from rest, gaining angular speed at the constant rate α1 through the first 400 rad and then losing angular speed at the constant rate α1 until it is again at rest. the magnitude of the centripetal acceleration of any portion of the disk is not to exceed 405 m/s2. (a) what is the least time required for the rotation? (b) what is the corresponding value of α1?

(A) 43.55 s

(B)  1.69 rad/s^{2}

Explanation:

radius (r) = 0.3 m

rotating trough (θ) = 800 rad

initial angular speed (ω°) = 0

maximum centripetal acceleration (α) = 405 m/s^{2}

rate of speed gain = α1

rate of speed loos = α1

(A) we fist have to get the maximum angular speed from the equation below.

maximum centripetal acceleration (α) =

where ω = maximum angular speed

405 =  

ω = = 36.74 rad/s

from the equation of angular motion for constant angular acceleration

  θ= x t we can get the time taken to attain maximum speed

where

400 = x t

t = (400 x 2) / 36.74

time taken to attain maximum speed (t) = 21.77 s

since the disk gains speed at the same constant rate as it looses it, the time taken to attain the maximum speed is equal to the time taken to decelerate back to rest, the total time = 2 x time taken to attain maximum speed (t)

total time = 2 x 21.77 = 43.55 s

(B) from the equation of angular motion for constant angular acceleration

     ω=  ω' +  α1 x t

     36.74 = 0 + ( α1 x 21.77)

      α1 = 36.74 /21.77 = 1.69 rad/s^{2}

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​

there is no correct list among the choices you've provided.

the list might look something like this:

-- baby human

-- piccolo

-- flute

-- soprano singer

-- trumpet

-- tenor singer

-- trombone

-- baritone singer

-- baritone horn

-- bass singer

-- tuba

since i had to make up the list myself, i made it easy on myself, and i didn't try to shuffle the string instruments and woodwinds into it too.