A merry-go-round makes 120 revolutions per mi | vedclass

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

Question

(C) Given: Initial frequency $n_1 = 120 \ rev/min = 2 \ rev/s$. Initial angular velocity $\omega_0 = 2\pi n_1 = 2\pi(2) = 4\pi \ rad/s$. Final angular

Vedclass · Accepted Answer

$2\pi \ s$,$2\pi$ revolutions

Vedclass · Answer

(C) Given: Initial frequency $n_1 = 120 \ rev/min = 2 \ rev/s$. Initial angular velocity $\omega_0 = 2\pi n_1 = 2\pi(2) = 4\pi \ rad/s$. Final angular velocity $\omega = 0$. Angular retardation $\alpha = -2 \ rad \ s^{-2}$.Using the equation of motion $\omega = \omega_0 + \alpha t$:$0 = 4\pi + (-2)t \implies 2t = 4\pi \implies t = 2\pi \ s$.Now,to find the number of revolutions,we first find the total angular displacement $	heta$:$	heta = \omega_0 t + \frac{1}{2} \alpha t^2 = (4\pi)(2\pi) + \frac{1}{2}(-2)(2\pi)^2 = 8\pi^2 - 4\pi^2 = 4\pi^2 \ rad$.The number of revolutions $N = \frac{	heta}{2\pi} = \frac{4\pi^2}{2\pi} = 2\pi$ revolutions.

$A$ merry-go-round makes $120$ revolutions per minute. $A$ child sitting on it starts crying,so the merry-go-round is slowed down with a retardation of $2 \ rad \ s^{-2}$. How long will it take for the merry-go-round to come to a stop? How many revolutions will it make before coming to a stop?

Similar Questions

$A$ particle of mass $m$ moves along a circle of radius $r$ with constant tangential acceleration. If the kinetic energy $E$ of the particle becomes three times by the end of the third revolution after the beginning of the motion,then the magnitude of the tangential acceleration is:

$A$ wheel initially at rest,begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first $2 \ s$ and a further angle $\theta_2$ in the next $2 \ s$,the ratio $\theta_1 : \theta_2$ is

$A$ 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 .........$\pi$.

$A$ 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:

$A$ wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{\circ}$ in time $t \ s$. The increase in angle through which it rotates in the next $2t \ s$ is (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module