A homogeneous disc with a radius 0.2 m and mass 5 kg rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula ω = 2 + 6t. The tangential force applied to the rim of the disc is
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Question

A homogeneous disc with a radius 0.2 m and mass 5 kg rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula ω = 2 + 6t. The tangential force applied to the rim of the disc is

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G1 Physics · Accepted Answer

ω=2+6t, so α=6 rad/s². For a disc I=½MR²=0.1 kg·m². Thus τ=Iα=0.6 N·m and F=τ/R=3 N. Hence C. Write translation ΣF=Ma and rotation Στ about CM=I about CMα, together with the no-slip relation v of CM=ωR and a of CM=αR whenever pure rolling applies. Solving the equations for the shown geometry gives 3N..