Answer:
a) The angular acceleration is 1.875 radians per square second.
b) The time taken by the disk to reach the final angular speed is 8 seconds.
Explanation:
a) Let suppose that the disk accelerates uniformly, given that initial and final angular speed ([tex]\omega_{o}[/tex], [tex]\omega_{f}[/tex]), in radians per second, and change in angular position ([tex]\Delta \theta[/tex]), in radians, are known. The angular acceleration ([tex]\alpha[/tex]), in radians per square second, are found by using this expression:
[tex]\alpha = \frac{\omega_{f}^{2}-\omega_{o}^{2}}{2\cdot \Delta \theta}[/tex] (1)
If we know that [tex]\omega_{o} = 0\,\frac{rad}{s}[/tex], [tex]\omega_{f} = 15\,\frac{rad}{s}[/tex] and [tex]\Delta \theta = 60\,rad[/tex], then the angular acceleration of the disk is:
[tex]\alpha = \frac{\omega_{f}^{2}-\omega_{o}^{2}}{2\cdot \Delta \theta}[/tex]
[tex]\alpha = 1.875\,\frac{rad}{s^{2}}[/tex]
The angular acceleration is 1.875 radians per square second.
b) The time taken by the disk to reach the final angular velocity is determined by the following kinematic formula:
[tex]t = \frac{\omega_{f}-\omega_{o}}{\alpha}[/tex] (2)
Where [tex]t[/tex] is the time, in seconds.
If we know that [tex]\omega_{o} = 0\,\frac{rad}{s}[/tex], [tex]\omega_{f} = 15\,\frac{rad}{s}[/tex] and [tex]\alpha = 1.875\,\frac{rad}{s^{2}}[/tex], then the time taken by the disk is:
[tex]t = \frac{\omega_{f}-\omega_{o}}{\alpha}[/tex]
[tex]t = 8\,s[/tex]
The time taken by the disk to reach the final angular speed is 8 seconds.
