A disk rotates about its central axis starting from rest and accelerates with co

Question

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 10 rev/s. 75 revolutions later, its angular speed is 24 rev/s.

(a) Calculate the angular acceleration.
___ rev/s2

(b) Calculate the time required to complete the 75 revolutions mentioned.
___s

(c) Calculate the time required to attain the 10 rev/s angular speed.
___s

(d) Calculate the number of revolutions from rest until the time the disk attained the 10 rev/s angular speed.
___rev

Explanation / Answer

here,

initial angular speed , w0 = 10 rev/s

w0 = 62.8 rad/s

number of revolution , n = 75

theta = n*2*pi

theta = 471 rad

the angular speed , w = 24 rev/s

w = 150.72 rad/s

a)

let the accelration be a

using third equation of motion

w^2 - w0^2 = 2*theta*a

24^2 - 10^2 = 2*75*a

a = 3.17 rad/s^2

the angular accelration is 3.17 rad/s^2

b)

let the time required be t

using first equation of motion

w = wo + a*t

24 = 10 + 3.17 * t

t = 4.42 s

thetime required to complete the 75 revolutions is 4.42 s

c)

let the time taken be t'

using first equation of motion

w0 = 0 + a*t'

10 = 3.17*t

t = 3.15 s

the time taken to attain 10 rev/s is 3.15 s

d)

the number of revolutions from rest until the time the disk attained the 10 rev/s angular speed ,

theta' = 0 + 0.5 * a*t'^2

theta' = 0 + 0.5 * 3.17 * 3.15^2

theta' = 15.73 rev

the number of revolutions from rest until the time the disk attained the 10 rev/s angular speed is 15.73 rev

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