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The equation ωz(t) = C - Dt2 gives the angular velocity of a rotating particle, where C = 4.20 rad/s and D = 0.250 rad/s3. Express its angular accleration in the form α(t) = ?
A sprocket has a circumference of 56.55 cm measured along the teeth tips. The angular velocity of the sprocket is modeled by ω = [6.0 + (1/6)t²] rad/s , where the units of t is s. Determine the tangential acceleration at the tip of a tooth on the sprocket when t = 9.0 s.
A shaft has an angular velocity function ω = (25 - t2) rad/s, where t is measured in seconds. Calculate Δθ for the shaft between t = 0s and the time when the direction of the spinning shaft is reversed.
A vehicle is fitted with a tubeless, 1160 mm diameter tire. The vehicle is driven at a speed of 80 miles per hour. A repair strip used in puncture repair is visible at the outer edge (threaded area) of the tire. Determine the speed of the visible section of the repair strip when it is located at the bottom of the tire.
A shaft acted on by multiple torques has angular velocity given by ω = (5 - 0.2t2), t being in seconds. When will the shaft experience reversal in its direction of rotation?
