CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Rotational Inertia

A uniform rin...

Question

A uniform ring of radius R is given a backspin of angular velocity $V_{o} / 2 R$ and thrown on a horizontal rough surface with the velocity of the centre to be $V_{o}$ . Find the velocity of the centre of the ring when it starts pure rolling.

Open in App

Solution

We know about point any point $P$ on ground Angular momentum will be conserved. As torque due to friction blows off.
$V = r w$
$I_{c m} = M v^{2} v_{i} = v_{0} v_{f} = v w_{i} = - \frac{v_{0}}{2 R} w_{f} = w_{p} = c o n s t a n t m v_{0} r - m r^{2} \times \frac{v_{0}}{2 v} = m v r + m r^{2} w \Rightarrow v_{0} - \frac{v_{0}}{2} = 2 v \Rightarrow v = \frac{v_{0}}{4}$
$∴$ Final velocity is $\frac{v_{0}}{4}$ in forward direction.

Suggest Corrections

thumbs-up

0

Similar questions

Q. A uniform ring of radius

R

is given a back spin of angular velocity

\frac{V_{0}}{2 R}

and thrown on a horizontal rough surface with velocity of centre to be

V_{0}

. The velocity of the centre of the ring when it starts pure rolling will be

Q. A uniform ring of radius

R

if given a back spin of angular velocity

V_{0} / 2 R

and thrown on a horizontal rough surface with velocity of centre the be

V_{0}

. The velocity of the centre of the centre of the ring when it starts pure rolling will be

Q. A solid ball of mass m and radius R is given linear velocity V and no angular velocity and placed on a rough surface. what is the velocity of centre of mass when ball starts pure rolling.

Q. A uniform circular ring of mass

M

R

with a particle of mass

m = \frac{M}{2}

rigidly attached to its topmost point is placed on a rough horizontal surface. When a negligible push is given to the ring, it starts rolling without slipping relative to the rough horizontal surface as shown. Now, when the particle is getting at the right end of the horizontal diameter of the ring, choose the correct option(s).

J

is applied on a ring of mass

m

along a line passing through its centre

O

. The ring is placed on a rough horizontal surface. The linear velocity of centre of ring, once it starts rolling without slipping, is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Moment of Inertia

PHYSICS

Watch in App

explore_more_icon

Explore more

Rotational Inertia

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon