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 6.4 rev/s; 60 revolutions later, its angular speed is 17 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 60 revolutions, (c) the time required to reach the 6.4 rev/s angular speed, and (d) the number of radians from rest until the time the disk reaches the 6.4 rev/s angular speed. A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 6.4 rev/s; 60 revolutions later, its angular speed is 17 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 60 revolutions, (c) the time required to reach the 6.4 rev/s angular speed, and (d) the number of radians from rest until the time the disk reaches the 6.4 rev/s angular speed. A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 6.4 rev/s; 60 revolutions later, its angular speed is 17 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 60 revolutions, (c) the time required to reach the 6.4 rev/s angular speed, and (d) the number of radians from rest until the time the disk reaches the 6.4 rev/s angular speed.

Explanation / Answer

a) let the initial angular speed be , and the final speed is .

Converting 6.4 rev/s into rad/s = 6.4 rev/s * 2rad/rev = 40.19 rad/s

= 40.19 rad/s

Converting 17 rev/s into rad/s = 17 rev/s * 2rad/rev = 106.76 rad/s

=106.76 rad/s

= 60 rev * (2rad/rev) = 376.8 rad

we know,

² = ² + 2

Solving for -

= (² -²)/ 2

= (106.76² -40.19²)/ 2 * 376.8 rad

= 12.97 rad/s^2

= 2.06 rev/s^2

angular acceleration = 2.06 rev/s^2

b)

We Know ,

= + t

t = ( - ) /

t = (106.76 rad/s - 40.19 rad/s) / 12.97 rad/s²

t = 5.13s
time required to complete the 60 revolutions t = 5.13s

c)

Since the acceleration is constant, we can use -

= + t

where = 0 and = 40.19 rad/s

solving for t =

t = ( - ) /

t = 40.19 / 12.97

t = 3.09 s
Time required to reach the 6.4 rev/s angular speed t = 3.09 s

d)

We Know,

² = ² + 2

= (²- ²) / 2

= [(44rad/s)² - 0)] / (2 x 12.97 rad/s²)

= 74.63 rad

The number of radians from rest until the time the disk reaches the 6.4 rev/s angular speed = 74.63 rad

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