If an ant is starting from 0 radians, and travels all the way to 4.5 radians in 18 seconds, what is angular velocity? If the same ant then slows down back to 0 rad/s in 3 seconds what is its angular acceleration?

Answer :

Answer:

  • Angular velocity is 0.25 rad/s
  • Angular acceleration is 0.017 rad/s²

Explanation:

Given;

initial angular displacement, θ₁ = 0 radians

final angular displacement, θ₂ = 4.5 radians

Angular velocity is calculated as;

[tex]\omega = \frac{\delta \theta}{\delta t}= \frac{4.5 -0}{18} \\\\\omega = 0.25 \ rad/s[/tex]

Angular acceleration is calculated as;

[tex]\alpha = \frac{\delta \omega}{\delta t} = \frac{\omega _f - \omega_i}{t_2 -t_1}[/tex]

where;

[tex]\omega_f[/tex] is the final angular velocity = 0 rad/s

[tex]\omega _i[/tex] is the initial angular velocity = 0.25 rad/s

t₂ is the final time of the motion = 3 seconds

t₁ is the initial time of the motion = 18 seconds

[tex]\alpha =\frac{\omega _f - \omega_i}{t_2 -t_1} \\\\\alpha = \frac{0 - 0.25}{3-18} \\\\\alpha = 0.017 \ rad/s^2[/tex]

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