Question

A cord s wrapped around the rim of a solid uniform wheel 0.22 m in radius and of mass 8.60 kg . A steady horizontal pull of 50.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. 

Part A 

Compute the angular acceleration of the wheel

Part B 

Compute the angular acceleration of the part of the cord that has already been pulled off the wheel.

Part C 

Find the magnitude of the force that the axie exerts on the wheel. 

Part D 

Find the direction of the force that the axle exerts on the wheel. 

 Part E 

Which of the answers in parts (A), B), (C) arid ID) would change if the pull were upward instead of horizontal? 

Answer 1

A]

Total torque, Στ=I*α
moment of inertia, I=m*r²/2
50*r = 8.60*r²*α / 2
α = 100 / (8.60*0.220)
α = 52.85 rad/s²

B] magnitude of acceleration = 52.85*0.220 = 11.63 m/s²

C] magnitude of Force = sqrt(50²+[8.6²*9.81²]) =  98 N

D) Direction of the force that the axel exerts on the wheel = tan^-1([8.6*9.81]/[2*50]) = tan^-1[84.37 / 100]
40.15^o below horizontal