Respuesta :
Answer:
544.68604 rad/s²
Explanation:
m = Mass of disk = 1.06 kg
R = Radius of disk = 0.433 m
T = Tension
[tex]T_2[/tex] = 167 N
[tex]T_1[/tex] = 42 N
Moment of inertia is given by
[tex]I=\dfrac{1}{2}mR^2\\\Rightarrow I=\dfrac{1}{2}\times 1.06\times 0.433^2[/tex]
The resultant torque of the system will be given by
[tex](T_2-T_1)R=\tau\\\Rightarrow (T_2-T_1)R=I\alpha\\\Rightarrow \alpha=\dfrac{(T_2-T_1)R}{I}\\\Rightarrow \alpha=\dfrac{(167-42)\times 0.433}{\dfrac{1}{2}\times 1.06\times 0.433^2}\\\Rightarrow \alpha=544.68604\ rad/s^2[/tex]
The angular acceleration of the disk is 544.68604 rad/s²
The change in the velocity with respect to time is called acceleration.
The acceleration depends on the following:-
- Velocity
- Time
According to the question, the data is as follows:-
m = 1.06 kg
R = 0.433 m
T = Tension, T1 = 167 N , T2= 42 N
To calculate we will use the formula of the moment of inertia i.e
[tex]I =\frac{1}{2}mr^2[/tex]
After putting the value,
[tex]I = \frac{1}{2} *1.06*0.433^2[/tex]
The resultant torque of the system will be given by
[tex]torque = (T_2-T_1)R[/tex]
[tex]Ia = (T_2-T_1)R[/tex]
[tex]a =\frac{(T_2-T_1)R}{I}[/tex]
[tex]a= \frac{(167-42)*0.433}{\frac{1}{2}*1.06*0.433^2}[/tex]
After solving the equation, a is = 544.68604
Hence, The angular acceleration of the disk is 544.68604 rad/s²
For more information, refer to the link:-
https://brainly.com/question/19247046
