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 7.8 rev/s; 60 revolutions later, its angular speed is 25 rev/s. Calculate (a) the angular acceleration (rev/s^2), (b) the time required to complete the 60 revolutions, (c) the time required to reach the 7.8 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 7.8 rev/s angular speed. (a) Number Unit (b) Number Unit c) Number Unit d) Number Unit

Explanation / Answer

For part (a), let the initial angular speed be , and the final speed is . The value for 7.8 rev/s in rad/s is :

7.8 rev/s(2rad/rev) = 49rad/s

The value of (25rev/s) is found in the same way and is 157.07 rad/s (rounded). It takes 70 revolutions to get to this speed, and 60 revolutions is :

= 60 rev(2rad/rev) = 376.99rad

The angular acceleration is :

² = ² + 2

Solved for :

= (² - ²) / 2
= [(157.07rad/s)² - (49rad/s)²] / (2 x 376.99rad)
= 29.53 rad/s²

(b) The time fir this is found from :

= + t
t = ( - ) /
= (157.07rad/s - 49rad/s) / 29.53rad/s²
= 3.65s

(c) Since the acceleration is constant, the value from part (a) applies, so :

t = (49rad/s - 0) / 29.53rad/s²
= 1.65s

(d) The number of revolutions is the angle () the disk moves through from rest until it reaches 44rad/s :

² = ² + 2
= (²- ²) / 2
= [(49rad/s)² - 0)] / (2 x 29.53rad/s²)
= 40rad

40rad = 40rad(1.0rev / 2rad) = 6.36 revolutions.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.