Question

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 1

• Angular velocity is 0.25 rad/s

• Angular acceleration is 0.017 rad/s²

Step-by-step explanation:

Given;

initial angular displacement, θ₁ = 0 radians

final angular displacement, θ₂ = 4.5 radians

Angular velocity is calculated as;

`\omega = (\delta \theta)/(\delta t)= (4.5 -0)/(18) \\\\\omega = 0.25 \ rad/s`

Angular acceleration is calculated as;

`\alpha = (\delta \omega)/(\delta t) = (\omega _f - \omega_i)/(t_2 -t_1)`

where;

`\omega_f` is the final angular velocity = 0 rad/s

`\omega _i` 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

`\alpha =(\omega _f - \omega_i)/(t_2 -t_1) \\\\\alpha = (0 - 0.25)/(3-18) \\\\\alpha = 0.017 \ rad/s^2`