Respuesta :
Answer:
Angular displacement of the wheel, [tex]\theta=267.41\ rad[/tex]
Explanation:
It is given that,
Angular acceleration of the wheel, [tex]\alpha =6.7\ rad/s^2[/tex]
Final speed of the wheel, [tex]\omega_f=74.5\ rad/s[/tex]
Time taken, t = 4.5 s
Initially, it is required to find the initial angular velocity of the wheel. Using the first equation of rotational kinematics as :
[tex]\omega_f=\omega_o+\alpha t[/tex]
[tex]\omega_o[/tex] is the initial speed of the wheel
[tex]\omega_o=\omega_f-\alpha t[/tex]
[tex]\omega_o=74.5-6.7\times 4.5[/tex]
[tex]\omega_o=44.35\ rad/s[/tex]
Let [tex]\theta[/tex] is the angular displacement of each wheel during this time. Using the second equation of motion as :
[tex]\theta=\omega_o t+\dfrac{1}{2}\alpha t^2[/tex]
[tex]\theta=44.35\times 4.5+\dfrac{1}{2}\times 6.7\times (4.5)^2[/tex]
[tex]\theta=267.41\ rad[/tex]
So, the angular displacement of each wheel during this time is 267 radian.
