A hoop of radius r and mass m rotating with a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) When the hoop is placed on the surface,friction acts on it,creating a torque about any point $O$ on the surface. Since the net external torque abo

Vedclass · Accepted Answer

$\frac{r\omega_0}{2}$

Vedclass · Answer

(C) When the hoop is placed on the surface,friction acts on it,creating a torque about any point $O$ on the surface. Since the net external torque about point $O$ is zero,the angular momentum about $O$ is conserved.Initial angular momentum about $O$ is $L_i = I_{cm}\omega_0 + mvr = (mr^2)\omega_0 + m(0)r = mr^2\omega_0$.When the hoop ceases to slip,it undergoes pure rolling,so $v_{cm} = \omega r$.Final angular momentum about $O$ is $L_f = I_{cm}\omega + mv_{cm}r = (mr^2)\omega + m(v_{cm})r = mr^2(\frac{v_{cm}}{r}) + mv_{cm}r = mv_{cm}r + mv_{cm}r = 2mv_{cm}r$.Equating $L_i$ and $L_f$:$mr^2\omega_0 = 2mv_{cm}r$$v_{cm} = \frac{r\omega_0}{2}$.

$A$ hoop of radius $r$ and mass $m$ rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Similar Questions

Which air pollutant is responsible for the Bhopal gas tragedy?

$A$ square current-carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\vec{F}$,what is the net force on the remaining three arms of the loop?

Viruses have

Which of the following reagents are required to prepare $3$-ethylpentan-$3$-ol?

On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ before $B$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module