A wheel of radius 0.4 ,m can rotate freely ab | vedclass

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Question

(A) Given:
Radius of the wheel, $r = 0.4 \,m$
Angular acceleration, $\alpha = 8 \,rad \,s^{-2}$
Mass hung, $m = 4 \,kg$
Acceleration due to gravit

Vedclass · Accepted Answer

$2 \,kg \,m^2$

Vedclass · Answer

(A) Given:
Radius of the wheel, $r = 0.4 \,m$
Angular acceleration, $\alpha = 8 \,rad \,s^{-2}$
Mass hung, $m = 4 \,kg$
Acceleration due to gravity, $g = 10 \,m \,s^{-2}$
The torque $	au$ produced by the weight of the mass hanging from the rim is given by:
$	au = m \cdot g \cdot r$
Also, the torque is related to the moment of inertia $I$ and angular acceleration $\alpha$ by the equation:
$	au = I \cdot \alpha$
Equating the two expressions for torque:
$I \cdot \alpha = m \cdot g \cdot r$
Substituting the given values:
$I \cdot 8 = 4 	imes 10 	imes 0.4$
$I \cdot 8 = 16$
$I = \frac{16}{8} = 2 \,kg \,m^2$
Therefore, the moment of inertia of the wheel is $2 \,kg \,m^2$.

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