A pulley wheel that is 8.0 cm in diameter has a 5.6-m-long cord wrapped around i

Question

A pulley wheel that is 8.0 cm in diameter has a 5.6-m-long cord wrapped around it. Starting from rest, the rope is pulled with a constant acceleration of 6 cm/s2 (assume that the pulley is wide enough that the cord is only wrapped around the pulley and not around itself.    a) How many revolutions does the wheel make when the cord is completely unwound from the pulley?    b) What is the angular velocity of the wheel once the cord is unwound? A pulley wheel that is 8.0 cm in diameter has a 5.6-m-long cord wrapped around it. Starting from rest, the rope is pulled with a constant acceleration of 6 cm/s2 (assume that the pulley is wide enough that the cord is only wrapped around the pulley and not around itself.    a) How many revolutions does the wheel make when the cord is completely unwound from the pulley?    b) What is the angular velocity of the wheel once the cord is unwound?

Explanation / Answer

Given Diameter of the wheel, d = 8.0 cm = 8 *10^-2 m Radius of the wheel, r = 4 *10^-2 m Length of the cord wrapped, L = 5.6 m Acceleration of the rope , a = 6cm/s^2 = 6 *10^-2 m/s^2 a) The number of revolutions made by the wheel is      L = r?      ? = L/r = 5.6 m/( 4 *10^-2 m)      ? =  140 rev b) First we will calculate the veocity    since a = v^2/r 6 *10^-2 m/s^2 = v^2/4 *10^-2 m v = 0.048 m/s The angular velocity is    ? = v/r = (0.048 m/s)/4 *10^-2 m    ? = 1.2 rad/s    

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