A sphere rolls without slipping on a rough horizontal surface with centre of mass having constant speed v0 . If mass of the sphere is m and its radius is R , then what is the angular momentum of the sphere about the point of contact?

Question

A sphere rolls without slipping on a rough horizontal surface with centre of mass having constant speed v0 . If mass of the sphere is m and its radius is R , then what is the angular momentum of the sphere about the point of contact? (A) (5/2)mv0R (B) (7/5)mv0R (C) (3/5)mv0R (D) (1/2)mv0R

Tardigrade Admin · Accepted Answer

Assume the angular velocity of the sphere is

ω

, as the sphere is rolling without slipping

ω = \frac{v _{0}}{R}

Now Angular momentum about the lowest point is the sum of angular momentum of center of mass and the angular momentum due to rotation of the sphere

\Rightarrow m v_{0} R + I ω = m v_{0} R + \frac{2}{5} m R^{2} \frac{v _{0}}{R} = \frac{7}{5} m v_{0} R

Q. A sphere rolls without slipping on a rough horizontal surface with centre of mass having constant speed $v_{0}$ . If mass of the sphere is $m$ and its radius is $R$ , then what is the angular momentum of the sphere about the point of contact?

$\frac{5}{2} m v_{0} R$

$\frac{7}{5} m v_{0} R$

$\frac{3}{5} m v_{0} R$

$\frac{1}{2} m v_{0} R$

Q. A sphere rolls without slipping on a rough horizontal surface with centre of mass having constant speed v0​ . If mass of the sphere is m and its radius is R , then what is the angular momentum of the sphere about the point of contact?

25​mv0​R

57​mv0​R

53​mv0​R

21​mv0​R

Q. A sphere rolls without slipping on a rough horizontal surface with centre of mass having constant speed $v_{0}$ . If mass of the sphere is $m$ and its radius is $R$ , then what is the angular momentum of the sphere about the point of contact?

$\frac{5}{2} m v_{0} R$

$\frac{7}{5} m v_{0} R$

$\frac{3}{5} m v_{0} R$

$\frac{1}{2} m v_{0} R$