A bicycle slows down uniformly from Vo=8.40 m/s to rest over a distance of 115m.

Question

A bicycle slows down uniformly from Vo=8.40 m/s to rest over a distance of 115m. Each wheel has a diameter of 68.0 cm and a mass of 1.70kg. A. Determine the initial angular velocity of the wheels (24.7 rad/s). B. Determine the moment of inertia of each wheel (treat as a solid disk). C. Determine the initial rotational kinetic energy of each wheel (120J). D. Determine the total # of revolutions of each wheel (53.8 rev). E. Determine the angular acceleration of each wheel. F. Determine the time it takes the bike to come to a complete stop (27.4s)

Explanation / Answer

How to find initial angular velocity? A wind turbine is initially spinning at a constant angular speed. As the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.123 rad/s2. After making 2630 revolutions, its angular speed is 159 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up? oh boy haven't done these in a while... time to remember some formulas... a) ok, first off, you can use this equation: vf^2 = vo^2 + 2*a*d (159 rad/s)^2 = vo^2 + 2*(.123rad/s^2)*(2630*2*pi) vo^2 = 21215.90477 vo = 145.657 rad/s b) vf = vo +at 159rad/s = 145.657rad/s + (.123rad/s^2)*t t = 108.48s

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