Answer to Question #127188 in Physics for Ukachukwu blessing

Question #127188
A body on the circular orbit makes an angular displacement given by(t)= 2t²+5t+5r, if t is in seconds calculate the angular velocity at t= 2s
1
Expert's answer
2020-07-22T10:33:34-0400

By definition, the angular velocity is:


ω(t)=dϕ(t)dt\omega(t) = \dfrac{d\phi(t)}{dt}

where ϕ(t)=2t2+5t+5\phi(t) = 2t^2 + 5t + 5 is the angular displacement. Thus, have:


ω(t)=dϕ(t)dt=4t+5 (rad/s)\omega(t) = \dfrac{d\phi(t)}{dt} = 4t+5 \space (rad/s)

At t= 2s:


ω(2s)=42s+5=8+5=13 rad/s\omega(2s) = 4\cdot 2s + 5 = 8+5=13\space rad/s

Answer. 13 rad/s.


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