Ahorizontal platform in the form of a disk is supported only at its center a man of mass m, originally at rest at a distance d from the center, begins to walk with uniform velocity v in the circumferential direction, stopping after an interval of time t. plot the torque exerted on the support as a function of time

Please see the attached Figure

Explanation:

The torque exerted on the disk support will be the multiplication of the force applied (the person weight=mg) and the distance d of the person to the disk support (notice this distance is in the radial direction). Considering torque To=F*d*sen(90°)=F*d (90° is formed by the weight and the radial direction).  

The person begins walking to the circumferential direction, which means the constant velocity has also radial direction.  

If we consider d=D+r, being r the distance walked by the person and dr its differential. We can say dr=v*dt, and if we consider t=0 the time the person begins walking and a constant velocity, we have r=v*t from t=0 to t=T.

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