Two pulleys of different radii (labeled a and b) are attached to one another, so

Question

Two pulleys of different radii (labeled a and b) are attached to one another, so that they can rotate together about a horizontal axis through the center. Each pulley has a string wrapped around it with a weight hanging from it. The radius of the larger pulley is twice the radius of the smaller one (b = 2a A student observing this system states: “The larger mass is going to create a counterclockwise torque and the smaller mass a clockwise torque. The torque for each will be the weight times the radius, and since the radius of the larger pulley is double the radius of the smaller one, while the weight of the heavier mass is less than double the weight of the smaller one, the larger pulley is going to win. The net torque will be clockwise, and so the angular acceleration will be clockwise.” Do you agree or disagree with this statement? In either case, explain your reasoning.

Explanation / Answer

We are having two pulleys say A and B

Radius A pulley is double than radius of B .

rA = 2×rB.

Now , masses are hanging through string , torque can be generated in this way:

T = tension force × radius .

Hence larger radius pulley will have larger torque .

Larger mass is going to create a counterclockwise torque and smaller mass is going to create a clockwise torque.

Net torque (Tnet) =m×rA- m×rB

Net torque will be in clockwise direction .

As we now torque = force × radius .

Force = mass × acceleration .

So angular acceleration will also be in clockwise direction.

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