A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t)= (6.0 rad/s⁴)t².The time it takes to make 10 rev is: A)1.3 s B)2.1 s C)2.8 s D)3.3 s E)4.0 s

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Quizplus · Accepted Answer

To find the time it takes to make 10 revolutions, we need to integrate the angular acceleration to find the angular velocity and then integrate again to find the angular displacement. The angular acceleration is given by $\alpha(t) = 6.0t^2$. Integrating this with respect to time gives the angular velocity $\omega(t) = \int 6.0t^2 \, dt = 2.0t^3 + C$. Since the wheel starts from rest, the constant $C = 0$. Integrating the angular velocity gives the angular displacement $\theta(t) = \int 2.0t^3 \, dt = 0.5t^4$. Setting $\theta(t) = 10 \times 2\pi$ (since 10 revolutions is $10 \times 2\pi$ radians), we solve $0.5t^4 = 20\pi$ for $t$, which gives $t \approx 3.3$ seconds.

A Wheel Starts from Rest and Has an Angular Acceleration α\alphaα

A Wheel Starts from Rest and Has an Angular Acceleration $\alpha$