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3-2.Motion in Plane
normal
Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc, the distance through which $P$ moves in one full rotation of the disc is
A$2\pi R$
B$4\pi R$
C$8R$
D$\pi R$
Solution
Speed of point $P$ is given by$v_{p}=2 v \sin \theta / 2$
$=2 v \sin \frac{w t}{2}$
$\frac{d x}{d t}=2 v \sin \frac{w t}{2}$
$x=2 v \int_{0}^{T} \sin \frac{\omega t}{2}=\frac{8 v}{\omega}=8 R$
Standard 11
Physics
