A doughnut has a mass of 50 grams when it is 10 cm around. A machine has 12 doug

Question

A doughnut has a mass of 50 grams when it is 10 cm around. A machine has 12 doughnuts attached to a rotating arm that starts from rest and after 5 revolutions has obtained full speed and spins at 20 rpm. That arm is used to coat a chocolate stripe on the outside edge of the doughnut (a) what is the angular acceleration; (b) How much time did it take to get to full speed?; (c) what is the speed at which the chocolate is coating the doughnut? (e) What is the moment of inertia for the doughnut? (f) What torque is required to make the doughnut rotate? (g) How much energy is imparted to the spinning doughnut? (h) What is the angular momentum of the wheel?

Explanation / Answer

a] using equation of rotations, alpha = w^2/2theta = [20/60]^2/(2*5) = 0.011111 rev/s^2 = 0.011111*2pi rad/s^2

= 0.0698 rad/s^2

b] time taken t = w/a = [20/60]/0.011111 = 30 s answer

c] speed v = wr = [20/60]*2pi*0.10 = 0.2094 m/s

d] moment of inetia = mr^2 = 0.050*0.10^2 = 5*10^-4 kgm^2

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