Respuesta :
Answer:
Explanation:
Given
magnitude of centripetal acceleration is twice the magnitude of tangential acceleration
Suppose [tex]\theta [/tex] is theta angle rotated by electric drill
it is given that it starts from rest i.e. [tex]\omega _0=0[/tex]
suppose [tex]\omega [/tex] and [tex]\alpha [/tex] is the final angular velocity and angular acceleration
using rotational motion equation
[tex]\omega ^2-\omega _0^2=2\times \alpha \times \theta [/tex]
where [tex]\theta [/tex]=angle turned by drill
[tex]\omega _0[/tex]=initial angular velocity
[tex]\omega [/tex]=final angular velocity
[tex]\alpha [/tex]=angular acceleration
[tex]\omega ^2-0=2\times \alpha \times \theta [/tex]
[tex]\omega ^2=2\alpha \theta ---1[/tex]
It is also given that centripetal acceleration is twice the magnitude of tangential i.e.
[tex]\omega ^2r=\alpha \times r[/tex]
where r=radial distance of any point from axis of drill
i.e. [tex]\omega ^2=\alpha [/tex]
substitute this value to equation 1
we get
[tex]\theta =\frac{\omega ^2}{2\alpha }[/tex]
[tex]\theta =1\ rad[/tex]
