A wheel accelerates from rest to 59 rad/s at a rate of 74 rad/s².Through what angle (in radians)did the wheel turn while accelerating? A)24 rad B)19 rad C)48 rad D)30 rad

Question

Quizplus · Accepted Answer

Explanation:The wheel's angular acceleration is 74 rad/s^2 and its final angular velocity is 59 rad/s. We can use the following equation to find the angle through which the wheel turned while accelerating:θ = ωi*t + 1/2*α*t^2where:θ is the angle through which the wheel turned (in radians)ωi is the initial angular velocity (in rad/s)α is the angular acceleration (in rad/s^2)t is the time (in seconds)In this case, the initial angular velocity is 0 rad/s, the angular acceleration is 74 rad/s^2, and the final angular velocity is 59 rad/s. We can solve for the time using the following equation:ωf = ωi + α*t59 rad/s = 0 rad/s + 74 rad/s^2 * tt = 59 rad/s / 74 rad/s^2 = 0.8 sNow that we know the time, we can substitute it into the first equation to find the angle through which the wheel turned:θ = 0 rad/s * 0.8 s + 1/2 * 74 rad/s^2 * (0.8 s)^2θ = 24 radTherefore, the wheel turned through an angle of 24 radians while accelerating.

A Wheel Accelerates from Rest to 59 Rad/s at a Rate