Answer:
A,B and C
Explanation:
Statement A
At all times, angular velocity is [tex]\omega = 0\,{\rm{rad/s}[/tex]
Angular acceleration is the rate of change in angular velocity with respect to time.
Angular velocity and angular acceleration are related by
[tex]{\omega _{\rm{f}}} = {\omega _{\rm{i}}} + \alpha t[/tex]
Which when re-arranged becomes
[tex]\alpha = \frac{{{\omega _{\rm{f}}} - {\omega _{\rm{i}}}}}{t}[/tex]
There’s no change in angular velocity anytime when the angular velocity is [tex]\omega = 0\,{\rm{rad/s}}[/tex]
The equation can be modified as follows:
[tex]\begin{array}{c}\\\alpha = \frac{{0\,{\rm{rad/s}} - 0\,{\rm{rad/s}}}}{t}\\\\ = 0\\\end{array}[/tex]
Therefore, the angular acceleration becomes zero hence statement A is valid.
Statement B
Angular acceleration is the rate of change in angular velocity with respect to time.
Angular velocity and angular acceleration are related by
[tex]{\omega _{\rm{f}}} = {\omega _{\rm{i}}} + \alpha t[/tex]
Which when re-arranged becomes
[tex]\alpha = \frac{{{\omega _{\rm{f}}} - {\omega _{\rm{i}}}}}{t}[/tex]
There’s no change in angular velocity anytime when the angular velocity is [tex]\omega = 10\,{\rm{rad/s}}[/tex].The final and initial velocities remain the same.
The equation can be modified as follows:
[tex]\begin{array}{c}\\\alpha = \frac{{10\,{\rm{rad/s}} - 10\,{\rm{rad/s}}}}{t}\\\\ = 0\\\end{array}[/tex]
Therefore, the angular acceleration becomes zero and statement B is valid
Statement C
Angular velocity is defined as the change in the angular position with respect to time.
Angular velocity and angular displacement are related by
[tex]\theta = \omega t[/tex]
Which can also be modified as:
[tex]{\theta _{\rm{f}}} - {\theta _{\rm{i}}}[/tex]
Note that the final position is [tex]{\theta _{\rm{f}}}[/tex]and initial position is [tex]{\theta _{\rm{i}}}[/tex]
Modifying the equation to find the angular velocity we obtain
[tex]\omega = \frac{{{\theta _{\rm{f}}} - {\theta _{\rm{i}}}}}{t}[/tex]
When the angular displacement has the same value at all times, the equation becomes
[tex]\begin{array}{c}\\\omega = \frac{{{\theta _{\rm{i}}} - {\theta _{\rm{i}}}}}{t}\\\\ = 0\\\end{array}[/tex]
The angular velocity becomes zero.
Angular acceleration and angular velocity are related by
[tex]{\omega _{\rm{f}}} = {\omega _{\rm{i}}} + \alpha t[/tex]
The expression above can be rearranged as follows:
[tex]\alpha = \frac{{{\omega _{\rm{f}}} - {\omega _{\rm{i}}}}}{t}[/tex]
At all times, the angular velocity is [tex]\omega = 0\,{\rm{rad/s}}[/tex] hence initial and final velocities remain the same
We obtain
[tex]\begin{array}{c}\\\alpha = \frac{{0\,{\rm{rad/s}} - 0\,{\rm{rad/s}}}}{t}\\\\ = 0\\\end{array}[/tex]
Therefore, the angular acceleration becomes zero and statement C is valid.
Therefore, statements A,B and C are consistent .
