A wheel (radius = 0.25 m)is mounted on a frictionless,horizontal axis.The moment of inertia of the wheel about the axis is 0.040 kg⋅m².A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure.The object is released from rest.What is the magnitude of the acceleration of the 0.50-kg object? A)3.0 m/s² B)3.4 m/s² C)4.3 m/s² D)3.8 m/s² E)2.7 m/s²

Question

Quizplus · Accepted Answer

The force that drives the movement is provided by the weight of the hanging weight $F_g=mg=0.5\cdot9.8=4.9N$. 
The torque created by this force is $	au=rF_g=0.25\cdot4.9=1.225N\cdot m$.
The angular acceleration of the wheel is $\alpha=	au/I=1.225/0.040=30.625 rad/s^2$.
The linear acceleration of the hanging weight is $a=r\alpha=0.25\cdot30.625=7.656 m/s^2$.
The magnitude of the acceleration of the hanging weight is $a_m=\sqrt{a^2}=4.33 m/s^2 \approx \boxed{	extbf{(C) }4.3 m/s^2}$.

A Wheel (Radius = 0