A ceiling fan rotates about its own axis with | vedclass

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

Question

(C) Let the initial angular velocity be $\omega_0$ and uniform angular retardation be $\alpha$. Using the equation of rotational motion $\omega^2 = \o

Vedclass · Accepted Answer

$\frac{16 n}{15}$

Vedclass · Answer

(C) Let the initial angular velocity be $\omega_0$ and uniform angular retardation be $\alpha$. Using the equation of rotational motion $\omega^2 = \omega_0^2 - 2\alpha	heta$,where $	heta = 2\pi n$. At time $t$,$\omega = \frac{\omega_0}{4}$. So,$(\frac{\omega_0}{4})^2 = \omega_0^2 - 2\alpha(2\pi n) \implies \frac{\omega_0^2}{16} = \omega_0^2 - 4\pi n\alpha$. $4\pi n\alpha = \omega_0^2(1 - \frac{1}{16}) = \frac{15\omega_0^2}{16}$. Thus,$2\alpha = \frac{15\omega_0^2}{32\pi n}$. Now,for the fan to come to rest,final angular velocity $\omega_f = 0$. Let $n'$ be the total revolutions from switch off to rest. $0^2 = \omega_0^2 - 2\alpha(2\pi n')$. $2\alpha(2\pi n') = \omega_0^2$. Substituting $2\alpha$: $(\frac{15\omega_0^2}{32\pi n})(2\pi n') = \omega_0^2$. $\frac{15n'}{16n} = 1 \implies n' = \frac{16n}{15}$.

Similar Questions

$A$ billiard ball is hit by a cue at a point distance $h$ above the centre. It acquires a linear velocity $v_0$. Let $m$ be the mass and $r$ be the radius of the ball. The angular velocity acquired by the ball 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)

$A$ constant torque of $1000 \; Nm$ turns a wheel of moment of inertia $200 \; kg \cdot m^2$ about an axis through its centre. The wheel is at rest initially. Its angular velocity after $3 \; s$ is

$A$ uniform rod of length $l$ and mass $m$ is pivoted at point $A$. The rod is released from a horizontal position. If the moment of inertia of the rod about point $A$ is $ml^2/3$,then its initial angular acceleration is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module