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 4.10 rev/s; 70.0 revolutions later, its angular speed is 20.0 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 70.0 revolutions, (c) the time required to reach the 4.10 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 4.10 rev/s angular speed

svijs angular s A disk rotates about its central axis starting from rest and accelerates with constant anqular acceleration. At one time it is rotating at 4.10 revis; 70.0 revalutions later, its angular speed is 20.0 rexis. Calculate (a) the angular acceleration (revis), (b) the time required to completa the To.D revclutions, (c) the time required to reach the 4.10 rov's angular speed, and (d) the numher of revalutions from rest until the time the disk reaches the 4.10 revis angular speed (a) Number (b) Number (c) Number (d) Number

Explanation / Answer

4.10 rev/s = 25.77 rad/s

20 rev/s = 125.71 rad/s

(vf - vi)/t = acceleration

70 x 2pi = 440 radians (rounded)

s/((vi + vf)/2) = time

440/((25.77 + 125.71)/2) = 5.809 secs

a)

(125.71 - 25.77)/5.809 = 17.20 rad/s^2 = 2.737 rev/s^2

b)

What is the time required to complete the 70 revolutions.

Using above work = 5.809 secs

c)

What is the time required to reach the 4.10 rev/s angular speed

v/a = t

25.77/17.29

t = 1.498 secs

d)

What is the number of revolutions from rest until the time the disk reaches the 4.10 rev/s angular speed.

s = (vi + vf)/2 * t

(0 + 25.77)/2 * 1.498 = 19.30 radians = 3.07 rev

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