1. Two wheels (solid cylinders) are glued to each other and are symmetrically al

Question

1. Two wheels (solid cylinders) are glued to each other and are symmetrically aligned around a center hole. The small wheel has half the radius of the large wheel and the small wheel has a mass of m, the large wheel a mass of M. A rod is placed in the hole and the wheels can rotate freely around their center. See the figure below for 5 forces acting on the wheels. All of the forces are tangential except for one force that is at 25° to the tangent. a. Find the torques for each force. b. What is the magnitude of the net torque? c. What is the angular acceleration of the system? 2 F 25" 3 F 0.5 F

Explanation / Answer

mass of the small wheel is m

mass of the large wheel is M

radius of the large wheel is r

radius of the small wheel is r/2

===>

a)

torque, T1=r*F

torque, T2=r*0.5*F

torque, T3=r*2F*sin(90-25) = r*2F*sin(65)

and

torque, T4=(r/2)*3*F

b)

net torque,

Tnet= T3+T4-T1-T2

= r*2F*sin(65)+(r/2)*3*F-r*Fr*0.5*F

=(2*sin(65)+3/2-1+0.5)*r*F

=1.8*r*F

c)

Tnet = I*alpa

1.8*r*F=(M*r^2+(m*(r/2)^2)*alpa

1.8*r*F=(M+m/4)*r^2*alpa

1.8*F=(M+m/4)*r*alpa

===>

alpa=1.8*F/((M+m/4)*r)

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