Answer to Question #313957 in Physics for abby

Question #313957

The angular acceleration of a wheel is α = 9.0t4 – 5.0t2, with α

 in radians per second-squared and t in seconds. At time t = 0, the wheel has an angular velocity of +7 rad/s and an angular position of +5 rad. Write expressions for (a) the angular velocity (rad/s) and (b) the angular position (rad) as functions of time (s).


1
Expert's answer
2022-03-20T18:50:58-0400

Given:

α=9.0t45.0t2\alpha = 9.0t^4 – 5.0t^2

ω0=7rad/s\omega_0=7\:\rm rad/s

θ0=5rad\theta_0=5\:\rm rad

(a) the angular velocity

ω=αdt+ω0=(9.0t45.0t2)dt+7=1.8t51.7t3+7\omega=\int \alpha dt+\omega_0=\int (9.0t^4 – 5.0t^2) dt+7\\ =1.8t^5-1.7t^3+7

(b) the angular position

θ=ωdt+θ0=(1.8t51.7t3+7)dt+5=0.3t60.42t4+7t+5\theta=\int \omega dt+\theta_0=\int (1.8t^5 – 1.7t^3+7) dt+5\\ =0.3t^6-0.42t^4+7t+5


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