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

$A$ wheel is rotating at a rate of $900$ revolutions per minute about its axis. When the power source is cut off,it comes to rest in $1$ minute. The angular retardation of the wheel in $rad/s^2$ is:

In the following figure,$r_1 = 5 \, cm$ and $r_2 = 30 \, cm$. If the moment of inertia of the wheel is $5100 \, kg \cdot m^2$,then its angular acceleration will be:

$A$ rope is wound around a solid cylinder of mass $1 \,kg$ and radius $0.4 \,m$. What is the angular acceleration of the cylinder, if the rope is pulled with a force of $25 \,N$? (The cylinder is rotating about its own axis.)

$A$ disc has mass $M$ and radius $R$. How much tangential force should be applied to the rim of the disc so as to rotate the disc with angular velocity $\omega$ in time $t$?

If the external torque acting on a system is $ \tau = 0 $, then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module