Question

QUESTION 1 Find the uncertainty in the moment of interia Moment of interia of a disk depends on mass and radius according to this function m.r)-1/2 m r2 Your measured mass and radius have the following uncertainties 5m 329 kg and 5r086 m. What is is the uncertanty in moment of intería, δ·if the measured mass, m-2717 kg and the measured radius, r-646 m? Units are not needed in your answer. QUESTION 2 Find the uncertainty in the moment of interia Moment of interia of a disk depends on mass and radius according to this function Im.r)-1/2 m r2. Your measured mass and radius have the following uncertainties 5m 0.46 kg and 5r 047 m What is is the uncertainty in moment of intería, δ, if the measured mass, m-3 84 kg and the measured radius, r-1777 m? Units are not needed in your answer QUESTION 3 Find the uncertainty in a calculated electrical potential diference from the measurements of current and resistance. Electric potential difference depends on current and resistance according to this function VOR)-IR Your measured current and resistance have the following values and uncertainties l-75 Amps, δ, = o 9 Amps and R-879 Ohms and 5R = o 6 Ohms what is the uncertainty in the 5V? Units are not needed in your answer.

Answer 1

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I = 1/2 mr^2: delta m = 3.29 kg, delta_r = 0.86 m m = 27.17 kg, r = 6.46 m delta I/I = delta m/m + 2 delta r/r: I = 1/2 time4s 27.17 times (6.46)^2 I = 566.9 kgm^2 delta I/566.9 = 3.29/27.17 + 2 times 0.86/6.46 = 0.121 + 0.266 = 0.387 delta I = 566.9 times 0.387 = 219.5 delta I = 219.5 kg m^2 uncertainty in moment of inertia m = 3.84 kg, r = 17.77 m s_m = 0.46 kg, delta r = 0.47 m I = 1/2 times mr^2 = 1/2 times 3.84 times (17.77)^2 I = 606.3 kgm^2 delta I = 606.3[0.46/3.84 + 2 times 0.47/17.77] = 104.7 delta I = 104.7 kgm^2 V = 1R Rightarrow delta V/V = delta I/I + delta R/R I = 7.5A: R = 87.9 ohm delta I = 0.9A delta R = 0.6 ohm, v = 1R v = 7.5 times 87.9 v = 659.25v delta V = 659.25[0.9/7.5 + 0.6/87.9]