A pulley of radius 2 m is rotated about its axis by a force F=(20t-5t²) N (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m², the number of rotations made by the pulley before its direction of motion is reversed, is

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(2) more than 3 but less than 6. Torque: τ=FR=(20t-5t²)(2)=40t-10t². Angular acceleration: α=τ/I=(40t-10t²)/(10)=4t-t². Integrate from rest: ω=∫₀^t(4t-t²)dt=2t²-(t³)/3. The direction reverses when ω first returns to zero: 2t²=(t³)/3, so t=6 s. Angle turned up to then: θ=∫₀⁶(2t²-(t³)/3)dt=[(2t³)/3-(t⁴)/(12)]₀⁶=144-108=36 rad. Rotations: (36)/(2π)=5.73. More than 3 but less than 6.

A pulley of radius 2 m is rotated about its axis by a force F=(20t-5t²) N (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m², the number of rotations made by the pulley before its direction of motion is reversed, is

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