A uniform disc of mass m and radius R is pivo | vedclass

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

Question

(A) The torque $	au$ acting on the disc about the pivot point $P$ is due to the gravitational force $mg$ acting at the centre of mass $C$.When the li

Vedclass · Accepted Answer

$\frac{2 g \cos 	heta}{3 R}$

Vedclass · Answer

(A) The torque $	au$ acting on the disc about the pivot point $P$ is due to the gravitational force $mg$ acting at the centre of mass $C$.When the line $PC$ makes an angle $	heta$ with the horizontal,the perpendicular distance from $P$ to the line of action of the gravitational force is $R \cos 	heta$.Therefore,the torque is $	au = mg(R \cos 	heta)$.The moment of inertia $I$ of the disc about an axis passing through the pivot point $P$ (which is on the rim) is given by the parallel axis theorem: $I = I_{cm} + mR^2 = \frac{1}{2} mR^2 + mR^2 = \frac{3}{2} mR^2$.Using the relation $	au = I \alpha$,we have:$mg(R \cos 	heta) = \left( \frac{3}{2} mR^2 ight) \alpha$Solving for the angular acceleration $\alpha$:$\alpha = \frac{mgR \cos 	heta}{\frac{3}{2} mR^2} = \frac{2g \cos 	heta}{3R}$.

Similar Questions

What does the time rate of change of angular momentum represent?

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

An air compressor is powered by a $200\,rad\,s^{-1}$ electric motor using a $V-$belt drive. The motor pulley is $8\,cm$ in radius,and the tension in the $V-$belt is $135\,N$ on one side and $45\,N$ on the other. The power of the motor will be ...... $kW$.

$A$ torque of $50\, Nm$ acting on a wheel at rest rotates it through $200\, rad$ in $5\, s$. Calculate the angular acceleration produced. ........... $rad\, s^{-2}$.

$A$ wheel having a moment of inertia of $4 \,kg \cdot m^2$ about its symmetrical axis rotates at a rate of $240 \,rpm$ about it. The torque required to stop the rotation of the wheel in one minute is ............ $N \cdot m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module