a) At the bottom is a 3 step pulley; consisting ofthree wheels of different diam
ID: 2246247 • Letter: A
Question
a) At the bottom is a 3 step pulley; consisting ofthree wheels of different diameters.b) The rotating arm has two masses attached,and is screwed into the 3 step pulley. Whenthe pulley rotates, so does the rod.c) The string is wrapped around one of thewheels in the 3 step pulley and passes overthe smart pulley. The mass hanger is hooked into the loop at the end of the string.d) When the system is released, the mass hanger falls, turning the smart pulley, and the 3 step pulley withthe rod attached. e) Assume: that the smart pulley is very light, so its moment of inertia is negligible as compared to the moment of inertia of the 3 step pulley and rod.
a)when you drop the mass holder, the system rotates at angular acceleration ?. If you wrapped the string around a larger diameter pulley and dropped the mass holder, the acceleration of the system would be:
At the bottom is a 3 step pulley; consisting of three wheels of different diameters.b) The rotating arm has two masses attached, and is screwed into the 3 step pulley. When the pulley rotates, so does the rod.c) The string is wrapped around one of the wheels in the 3 step pulley and passes over the smart pulley. The mass hanger is hooked into the loop at the end of the stringed) When the system is released, the mass hanger falls, turning the smart pulley, and the 3 step pulley with the rod attached. e) Assume: that the smart pulley is very light, so its moment of inertia is negligible as compared to the moment of inertia of the 3 step pulley and rod. when you drop the mass holder, the system rotates at angular acceleration ?. If you wrapped the string around a larger diameter pulley and dropped the mass holder, the acceleration of the system would be: exactly ?? less than a? more than a? Suppose that you measured the moment of inertia of the system as I = 5.05 kg-m2. Assume the diameter of the pulley around which you wrap the string is d = 2.5 cm. In trial 1:the system is initially spinning at angular speed ?o = 9.27 rad/s. After you drop a disk of mass 856 g on it, the system rotates at ?f = 8.35 rad/s. Find: - the moment of inertia of the disk: kg-m2 - the radius of the disk: cm In trial 3: suppose the system is initially spinning at angular speed ?o = 2.05 rad/s. After you drop a cube of mass 786 g on it, the system rotates at ?f = 1.79 rad/s. Find: - the moment of inertia of the cube: kg-m2 - the length of one side of the cube: cmExplanation / Answer
a) Since the torque on the smart pulley increases (due to increase in mass m)
both angular acceleration and angular momentum must increase for a given
I, the moment of inertia of pullley and rod.
Let a = angular acceleration
w = angular velocity of 3 step pulley
T = torque on 3 step pulley
b) moving the masses outward on the rod increases I
For a given torque (m remains constant)
T = I a
After a time t then T * t = I a t = I w
For a fixed torque the product of I and w is constant
so the angular momentum remains constant even tho a decreases
due to the increase in I
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