Question

The specifications for a ceiling fan you have just bought indicate that the total moment of inertia of its blades is 0.23 kg · m2 and they experience a net torque of 2.8 N · m.

(a) What is the angular acceleration of the blades in rad/s2? rad/s2

(b) When the blades rotate at 205 rpm, what is the rotational kinetic energy, in joules? J

Answer 1

Answer:(a)12.17 rad/s

Explanation:

Given

Moment of Inertia $I=0.23 kg.m^2$

Torque $T=2.8 N-m$

(a)Torque is given by Product of Moment of inertia and angular acceleration

$T=I\cdot \alpha$

$2.8=0.23\cdot \alpha$

$\alpha =\frac{2.8}{0.23}=12.17 rad/s$

(b)RPM of blades $N=205 rpm$

angular velocity $\omega =\frac{2\pi N}{60}$

$\omega =\frac{2\pi 205}{60}=21.47 rad/s$

Rotational Kinetic Energy $=\frac{I\omega ^2}{2}$

$=\frac{0.23\times (21.47)^2}{2}=53.01 J$