An electric motor is started from rest to pro | vedclass

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

Question

(D) Given angular acceleration: $\alpha = 3t - t^2$. Since $\alpha = \frac{d\omega}{dt}$,we have $d\omega = (3t - t^2) dt$. Integrating from $t = 0$ t

Vedclass · Accepted Answer

$\frac{10}{3} \ rad/s$

Vedclass · Answer

(D) Given angular acceleration: $\alpha = 3t - t^2$. Since $\alpha = \frac{d\omega}{dt}$,we have $d\omega = (3t - t^2) dt$. Integrating from $t = 0$ to $t = 2 \ s$ (the time when acceleration becomes zero): $\omega = \int_{0}^{2} (3t - t^2) dt = [\frac{3t^2}{2} - \frac{t^3}{3}]_{0}^{2}$. $\omega = (\frac{3(4)}{2} - \frac{8}{3}) = 6 - \frac{8}{3} = \frac{18 - 8}{3} = \frac{10}{3} \ rad/s$. Since the angular acceleration is zero for $t > 2 \ s$,the angular velocity remains constant at $\frac{10}{3} \ rad/s$ for all $t \ge 2 \ s$. Therefore,the angular velocity after $6 \ s$ is $\frac{10}{3} \ rad/s$.

An electric motor is started from rest to produce a torque. It acquires an angular acceleration given by $\alpha = 3t - t^2$. The angular acceleration becomes zero after $2 \ s$. Calculate the angular velocity after $6 \ s$.

Similar Questions

$A$ 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 $t$?

$A$ disc is rotating with an angular velocity $\omega_0$. $A$ constant retarding torque is applied on it to stop the disc. The angular velocity becomes $\frac{\omega_0}{2}$ after $n$ rotations. How many more rotations will it make before coming to rest?

$A$ solid cylinder of mass $2\; kg$ and radius $4\; cm$ is rotating about its axis at the rate of $3\; rpm$. The torque required to stop after $2\pi$ revolutions is

When a ceiling fan is switched off,its angular velocity reduces to $50\%$ while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

If there is a change of angular momentum from $1 \, J \cdot s$ to $4 \, J \cdot s$ in $4 \, s$, then the torque is

Vedclass Test Series

Exam Paper Generator

Online Exam Module