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A Helicopter’s blades are speeding up. They go from 60 rad/s to 80 rad/s. If the angular acceleration is 10.0 rad/s^2, What is the total angle the blades have gone through?



Answer :

Answer:

The total angle = 140 rad.

Explanation:

We can find the total angle the blades have gone through by using the rotational motion formulas:

[tex]\boxed{\omega=\omega_o+\alpha t}[/tex]

[tex]\boxed{\theta=\theta_o+\omega_ot+\frac{1}{2} \alpha t^2}[/tex]

where:

  • [tex]\omega[/tex] = final angular velocity
  • [tex]\omega_o[/tex] = initial angular velocity
  • [tex]\alpha[/tex] = angular acceleration
  • [tex]t[/tex] = time
  • [tex]\theta[/tex] = final position
  • [tex]\theta_o[/tex] = initial position

Given:

  • [tex]\omega_o[/tex] = 60 rad/s
  • [tex]\omega[/tex] = 80 rad/s
  • [tex]\alpha[/tex] = 10.0 rad/s²
  • [tex]\theta[/tex] = 0

[tex]\omega=\omega_o+\alpha t[/tex]

[tex]80 = 60 +10t[/tex]

[tex]10t=80-60[/tex]

[tex]\bf t=2\ s[/tex]

[tex]\theta=\theta_o+\omega_ot+\frac{1}{2} \alpha t^2[/tex]

  [tex]=0+60(2)+\frac{1}{2} (10)(2)^2[/tex]

  [tex]=\bf 140\ rad[/tex]

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