Respuesta :
Answer:
The angle and angular velocity at time 4.00 are 5.35 rev and 1.81 rev/s.
Explanation:
Given that,
Angular velocity = 5.40 rad/s
Time t = 0.000 sec
Angular acceleration = 1.50 rad/s^2
(a). We need to calculate the angle at time t = 4.00 s
Using formula for angle
[tex]\theta=\omega_{0}t+\dfrac{1}{2}\alpha t^2[/tex]
Where, [tex]\omega_{0}[/tex]=angular velocity
[tex]\alpha[/tex]=angular acceleration
t = time
Put the value into the formula
[tex]\theta=5.40\times4.00+\dfrac{1}{2}\times1.50\times(4.00)^2[/tex]
[tex]\theta=33.6\ rad[/tex]
[tex]\theta=\dfrac{33.6}{2\pi}\ rad[/tex]
[tex]\theta=5.35\ rev[/tex]
(b). We nee to calculate the angular velocity at 4.00 s
Using formula of angular velocity
[tex]\omega=\omega_{0}+\alpha t[/tex]
[tex]\omega =5.40+1.50\times4.00[/tex]
[tex]\omega=11.4\ rad/s[/tex]
[tex]\omega=\dfrac{11.4}{2\pi}\ rad/s[/tex]
[tex]\omega=1.81\ rev/s[/tex]
Hence, The angle and angular velocity at time 4.00 are 5.35 rev and 1.81 rev/s.
