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Intuition for COM

for pure roll...

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for pure rolling ofround object as shown the velocity of centre of mass i

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is velocity of centre of mass of a purely rolling body then velocity of lowest point of that body is :

Q. A uniform disc of mass m and radius R is projected horizontally with velocity

v_{0}

on a rough horizontal floor, so that it starts. off with a purely sliding motion at t = 0. After

t_{0}

seconds, it acquires a purely rolling motion as shown in figure. The velocity of the centre of mass of the disc at

t_{0}

.

Q. A wheel rolls purely on the ground. If the velocity of a point

^{'} P^{'}

as shown on the periphery of a body has a velocity equal to the velocity of the centre of mass of the body. Find

θ = ?

.

Q. A uniform disc of mass and radius

R

is projected horizontally with velocity

v_{c}

on a rough horizontal floor so that it starts off with a pure sliding motion at

t = 0

t_{0}

second it acquires pure rolling motion as shown in figure. Calculate the velocity of the centre of mass of the disc at

t_{0} .^{'} μ^{'}

is the coefficeient of friction.

Q. A thin spherical shell of mass

M

R

as shown in the figure slips on a rough horizontal plane. At the same instant, it has translational velocity

v_{0}

and rotational velocity about the centre

\frac{3 v_{0}}{R}

. Find the translation velocity after the shell starts pure rolling.

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