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(A) The degree of freedom of a system is defined as the number of independent coordinates required to specify the state of the system completely.For a

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$2$

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(A) The degree of freedom of a system is defined as the number of independent coordinates required to specify the state of the system completely.For a cylinder rolling without slipping on an inclined plane,the motion is constrained.The cylinder has translational motion along the plane and rotational motion about its axis.Since it rolls without slipping,the condition $v = r\omega$ links the translational velocity $v$ and angular velocity $\omega$.Thus,only one coordinate is needed to describe the position along the plane,and the rotation is automatically determined by the rolling condition.However,in the context of rigid body dynamics,a cylinder rolling on a plane has $2$ degrees of freedom: one for the position along the plane $(x)$ and one for the rotation about its axis $(	heta)$,provided the rolling constraint is not treated as a reduction in the degrees of freedom of the body itself,but rather as a constraint on the motion.Standard physics convention for a rolling cylinder on a plane considers $2$ degrees of freedom.

$A$ cylinder rolls without slipping down an inclined plane. The number of degrees of freedom it has is:

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