A disc of mass M kg and radius R m is rotat | vedclass

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

Question

(A) The moment of inertia of a disc about its central axis is $I = \frac{1}{2} M R^2$.Using the rotational analogue of Newton's second law,the torque

Vedclass · Accepted Answer

$\frac{M R \omega}{2 t}$

Vedclass · Answer

(A) The moment of inertia of a disc about its central axis is $I = \frac{1}{2} M R^2$.Using the rotational analogue of Newton's second law,the torque $	au$ is given by $	au = I \alpha$,where $\alpha$ is the angular acceleration.The torque applied by the tangential force $F$ is $	au = F 	imes R$.Equating the two expressions for torque: $F R = \frac{1}{2} M R^2 \alpha$.Solving for angular acceleration: $\alpha = \frac{2 F}{M R}$.Since the disc comes to rest from an initial angular speed $\omega$ in time $t$,the magnitude of angular deceleration is $\alpha = \frac{\omega}{t}$.Substituting $\alpha$ into the equation: $\frac{2 F}{M R} = \frac{\omega}{t}$.Solving for $F$: $F = \frac{M R \omega}{2 t}$.

$A$ disc of mass $M \ kg$ and radius $R \ m$ is rotating at an angular speed of $\omega \ rad/s$ when the motor is switched off. Neglecting the friction at the axle,the force that must be applied tangentially to the wheel to bring it to rest in time $t$ is ...............

Similar Questions

$A$ flywheel gains a speed of $540\ r.p.m.$ in $6\ s$. Its angular acceleration will be

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 ...... $kW$.

The instantaneous angular position of a rotating wheel is given by the formula $\theta (t) = 2t^3 - 6t^2$. At what time will the torque on this wheel be zero? $t = \dots \text{s}$

$A$ rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis (see figure). When released from the initial horizontal position,its instantaneous angular acceleration will be

$A$ wheel having a moment of inertia of $200 \ kg \cdot m^2$ about its axis passing through its center is rotated by a constant torque of $1000 \ N \cdot m$. What will be its angular velocity in $rad/s$ after $3 \ s$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module