Question

3) A horizontal circular platform can rotate around a vertical axis at its center with negligible friction. You decide to use the rotating platform to design a procedure that will allow you to determine the unknown rotational inertias of different objects, for example a bowl. You know the rotational inertia of the platform Ip. Which of the following procedures would serve your task? Comment on why. (More than one answer could be correct). Comment on the procedures that are not suitable and explain what is wrong with them (a) Exert a constant toque τ on the empty platform and measure its angular acceleration α. Then place the bowl on the platform and repeat the previous experiment, obtaining a Calculate the rotational inertia of the bowl using the expression B (b) Perform the same experiment as in (a) but use the expression I,-4( .1) PB (c) Spin the empty platform and measure its angular velocity a. While the platform is rotating place the bowl carefully on the platform at its center. Wait until the bowl rotates together with the platform. Measure the final angular velocity of the bowl-platform system aCalculate the rotational inertia of the bowl using the expression 1,-4( -1) (d) Perform the same experiment as in (c) but use the expressio) (e) Measure the mass of the platform mP , the mass of the bowl n's , the radius of the platform p and the radius of the bowl . Calculate the rotational inertia of the bowl using the expression 1,-IP、Mgr. Mr

Answer 1

The correct procedure is (C) Because rightarrow I_p wi = I_pB w_f (conservation og angular momentum) = (I_P + I_B) w_f Rightarrow I_B = I_p w_i/w_f - I_p OR I_B = I_p (w_i/w_f - 1) For (a) z = I p alpha p and tau = I_pB alpha P_B Rightarrow I_p = tau/alpha P and I_p + I_B = tau/alpha_pB so I_B = tau/alpha PB - tau/alpha p = tau (1/alpha_pB - 1/alpha p) so a is not correct for (b) I_B = I_P alpha _p(1/alpha_P_B - 1/alpha_p) = I_p [alpha_p/alpha_pB - 1]