Inner and outer radii of a spool are r and R | vedclass

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(C) For pure rolling,the velocity of the point of contact with the ground must be zero. When a force $F$ is applied to the thread wound on the inner r

Vedclass · Accepted Answer

Thread winds,spool moves to the right and friction acts rightwards.

Vedclass · Answer

(C) For pure rolling,the velocity of the point of contact with the ground must be zero. When a force $F$ is applied to the thread wound on the inner radius $r$ as shown,it creates a torque about the center of mass that tends to rotate the spool clockwise. As the spool rotates clockwise,the point of contact with the ground has a tendency to slip to the left. To oppose this,the static friction $f$ acts towards the right. However,let's analyze the torque about the point of contact $P$. The torque due to force $F$ is $	au_P = F(R-r)$ in the clockwise direction. Since this torque is non-zero,the spool will have an angular acceleration $\alpha$ in the clockwise direction. For pure rolling,the spool must move to the right with acceleration $a_{cm} = \alpha R$. Considering the forces: $F + f = m a_{cm}$ (where $f$ is friction acting to the right). Considering torque about the center of mass: $F r + f R = I \alpha$. Since the spool moves to the right and rotates clockwise,the thread winds further. Thus,the spool moves to the right and friction acts to the right.

Inner and outer radii of a spool are $r$ and $R$ respectively. $A$ thread is wound over its inner surface and placed over a rough horizontal surface. The thread is pulled by a force $F$ as shown in the figure. Then,in the case of pure rolling:

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