A flywheel is in the form of a solid circular | vedclass

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

Question

(B) The rotational kinetic energy $K_R$ is given by the formula $K_R = \frac{1}{2} I \omega^2$. For a solid circular disc,the moment of inertia $I = \

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(B) The rotational kinetic energy $K_R$ is given by the formula $K_R = \frac{1}{2} I \omega^2$. For a solid circular disc,the moment of inertia $I = \frac{1}{2} M R^2$. The angular velocity $\omega$ in radians per second is $\omega = 2 \pi n$,where $n$ is the frequency in revolutions per second. Given $M = 72 \ kg$,$R = 0.5 \ m$,and $n = \frac{70}{60} \ rev/s$. Substituting these values: $I = \frac{1}{2} 	imes 72 	imes (0.5)^2 = 36 	imes 0.25 = 9 \ kg \cdot m^2$. $\omega = 2 \pi 	imes \frac{70}{60} = \frac{7 \pi}{3} \ rad/s$. $K_R = \frac{1}{2} 	imes 9 	imes \left( \frac{7 \pi}{3} ight)^2 = \frac{1}{2} 	imes 9 	imes \frac{49 \pi^2}{9} = \frac{49 \pi^2}{2} \approx \frac{49 	imes 9.8696}{2} \approx 241.8 \ J$. Rounding to the nearest provided option,the value is $240 \ J$.

$A$ flywheel is in the form of a solid circular disc with a mass of $72 \ kg$ and a radius of $0.5 \ m$. If it rotates at $70 \ rpm$,its rotational kinetic energy is ........ $J$.

Similar Questions

If the angular velocity of a body rotating about a given axis increases by $20 \%$,then its kinetic energy of rotation will increase by: (in $\%$)

$A$ flywheel is making $\frac{3000}{\pi}$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400 \ kg \ m^2$,its rotational kinetic energy is

$A$ ring of mass $m$ and radius $r$ rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Its kinetic energy is

$A$ solid spherical ball of mass $1 \, kg$ and radius $3 \, cm$ is rotating with an angular velocity of $50 \, rad/s$ about an axis passing through its center. The rotational kinetic energy is:

$A$ thin rod of length $L$ is suspended from one end and rotates with $n$ revolutions per second. What will be the rotational kinetic energy of the rod?

Vedclass Test Series

Exam Paper Generator

Online Exam Module