Solved:
Answered by AI, Verified by Human Experts
A machine part rotates at. an angular speed of 0.060rad/s ; its speed is then increased to 2.2 rad/s at an angular acceleration of 0.70 rad/s . (a) Find the angle through which the part rotates before reaching this final speed.
A machine part rotates at. an angular speed of 0.060rad/s ; its speed is then increased to 2.2 rad/s at an angular acceleration of 0.70 rad/s . (a) Find the angle through which the part rotates before reaching this final speed.
Final answer:To find the angle through which a machine part rotates until its final speed, we calculate the time using the given initial and final angular velocities and angular acceleration, and then use the time to determine the rotated angle, resulting in approximately 3.1719 radians.Explanation:To find the angle through which a machine part rotates before reaching its final speed, we can use the formula θ = ω0t + 0.5αt2, where θ is the angle in radians, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time. However, the time is not directly given. We first need to find it using the formula ω = ω0 + αt, where ω is the final angular velocity. Rearranging the formula gives t = (ω - ω0)/α.Given ω0 = 0.060 rad/s, ω = 2.2 rad/s, and α = 0.70 rad/s2, let's calculate t: t = (2.2 - 0.060)/0.70 ≈ 3.057 s.Using this time in the angle formula: θ = (0.060)(3.057) + 0.5(0.70)(3.057)2 ≈ 3.1719 radians.Therefore, the part rotates through approximately 3.1719 radians before reaching its final speed....