We want to verify the rotational analogue of the relationship between force and

Question

We want to verify the rotational analogue of the relationship between force and acceleration as given by the equation Torque= I X angular acceleration. We will apply a constant torque to an aluminum disk by attaching a mass to a string wrapped around the disk and then hanging the mass over a frictionless pulley. The constant force due to gravity acting on the mass (F gravity=mg) is transferred to the disk by the string hanging over the pulley as a constant tension.

Explain what will happen to the disk when the mass hanging down over the pulley is released. Does this represent a constant torque? Explain your answer carefully.

Explanation / Answer

in rotational motion all the newton's equations in linear motion can be written with the corresponding analogue in rotation.eg. linear displacement transforms to angular displacement, linear acceleration to angular acceleration etc.

so S=ut + 1/2 at2 transforms to  = 0t + 1/2t2 and all other equations in similar manner ( represents angular displacement, 0 initial angular velocity,  angular acceleration)

In this question, the force acting on the wheel, the point of action of force and the perpendicular distance of the action of mass to centre of mass does not change.

Writing F=ma in rotational motion,  = I , the torque and angular acceleration is constant ,PROVIDED THE  STRING IS MASSLESS, IF STRING HASS MASS, I changes and angular acceleration varies with time, but the torque remains constant independent of whether the string has mass or not

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