Consider a 20, kg uniform circular disk of ra | vedclass

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

Question

(C) Given: Mass $m = 20\, kg$,Radius $R = 0.2\, m$,Force $F = 20\, N$,Initial angular speed $\omega_0 = 0$,Final angular speed $\omega = 50\, rad/s$.T

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) Given: Mass $m = 20\, kg$,Radius $R = 0.2\, m$,Force $F = 20\, N$,Initial angular speed $\omega_0 = 0$,Final angular speed $\omega = 50\, rad/s$.The torque $	au$ applied by the force $F$ is $	au = F \cdot R$.The moment of inertia of the disk about its center is $I = \frac{1}{2} mR^2$.Using $	au = I\alpha$,the angular acceleration $\alpha$ is:$\alpha = \frac{F \cdot R}{\frac{1}{2} mR^2} = \frac{2F}{mR} = \frac{2 	imes 20}{20 	imes 0.2} = \frac{2}{0.2} = 10\, rad/s^2$.Using the kinematic equation $\omega^2 = \omega_0^2 + 2\alpha\Delta	heta$:$(50)^2 = 0^2 + 2(10)\Delta	heta$$2500 = 20\Delta	heta$$\Delta	heta = 125\, rad$.Since one revolution corresponds to $2\pi \approx 6.28\, rad$,the number of revolutions $n$ is:$n = \frac{\Delta	heta}{2\pi} = \frac{125}{6.28} \approx 19.90$.Rounding to the nearest integer,$n = 20$.

Similar Questions

The moment of inertia of a body about a given axis is $1.2 \; kg \cdot m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1500 \; J$,an angular acceleration of $25 \; rad/s^2$ must be applied about that axis for a duration of: (in $; s$)

In the given figure,$r_1$ and $r_2$ are $10 \ cm$ and $20 \ cm$ respectively. If the moment of inertia of the wheel is $1500 \ kg \cdot m^2$,find the angular acceleration.

The thin rod shown below has mass $M$ and length $L$. $A$ force $F$ acts at one end as shown,and the rod is free to rotate about the other end in the plane of the force. The initial angular acceleration of the rod is ........

$A$ wheel is rotating about an axis through its centre at $720$ revolutions per minute. It is acted on by a constant torque opposing its motion for $8$ seconds until it comes to rest. The number of revolutions made by the wheel in the $8$ seconds is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module