A body rotating with uniform angular accelera | vedclass

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

Question

(A) Given: Initial angular velocity $\omega_0 = 0 	ext{ rad/s}$ (since it starts from rest).Angular displacement $	heta = 100 \pi 	ext{ rad}$.Time

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) Given: Initial angular velocity $\omega_0 = 0 	ext{ rad/s}$ (since it starts from rest).Angular displacement $	heta = 100 \pi 	ext{ rad}$.Time $t = 5 	ext{ s}$.Using the second equation of rotational motion: $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$.Substituting the values: $100 \pi = 0 + \frac{1}{2} \alpha (5)^2$.$100 \pi = \frac{25}{2} \alpha$.$\alpha = \frac{200 \pi}{25} = 8 \pi 	ext{ rad/s}^2$.Now,using the first equation of rotational motion: $\omega = \omega_0 + \alpha t$.$\omega = 0 + (8 \pi) 	imes 5 = 40 \pi 	ext{ rad/s}$.Thus,the angular speed at the end of $5 	ext{ s}$ is $40 \pi 	ext{ rad/s}$.

$A$ body rotating with uniform angular acceleration covers $100 \pi \text{ rad}$ in the first $5 \text{ s}$ after the start. Its angular speed at the end of $5 \text{ s}$ (in $\text{rad/s}$) is .........$\pi$.

Similar Questions

$A$ wheel has an angular acceleration of $3.0\, rad/s^2$ and an initial angular speed of $2.00\, rad/s$. In a time of $2\, s$,it has rotated through an angle (in radians) of:

If the angular velocity of a disc depends on the angle rotated $\theta$ as $\omega = \theta^2 + 2\theta$,then its angular acceleration $\alpha$ at $\theta = 1 \text{ rad}$ is ......... $\text{rad/sec}^2$.

The relative angular speed of the hour hand and the second hand of a clock is (in $rad/s$):

Identify the increasing order of the angular velocities of the following:
$1$. Earth rotating about its own axis
$2$. Hour hand of a clock
$3$. Second hand of a clock
$4$. Flywheel of radius $2 \ m$ making $300 \ rpm$

The angular acceleration of a body, moving along the circumference of a circle, is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module