Two uniform solid spheres have the same mass of 3 kg, but one has a radius of 0.25 m while the other has a radius of 0.8 m. Each can rotate about an axis through its center.

(a) What is the magnitude τ of the torque required to bring the smaller sphere from rest to an angular speed of 300 rad/s in 15 s?

(b) What is the magnitude F of the force that must be applied tangentially at the sphere's equator to provide that torque?

(c) What is the corresponding value of τ for the larger sphere?

(d) What is the corresponding value of F for the larger sphere?

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  1. I sphere = (2/5) mR^2

    I1 = (2/5)3 (.25)^2 = .075
    alpha = 300/15 = 20 radians/second^2
    Torque = I alpha = .075*20 = 1.5 Nm

    F1 = torque/R = 1.5/.25 = 6 N

    now big sphere
    I2 = (2/5)3 (.8)^2 = .768
    torque = I alpha = .768*20 = 15.36 Nm
    F2 = 15.36/.8 = 19.2 N

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