a turntable with a moment of inertia of 5.4x10^-3 rotates freely win an angular
ID: 1794528 • Letter: A
Question
a turntable with a moment of inertia of 5.4x10^-3 rotates freely win an angular speed of 33.3 rpm. Riding the rim of the turntable table, 15 cm from the center, is a 32-g mouse. A) if the mouse walks towards the center of the turntable, what is the angular speed of the mouse when is at half distance to the center? B) if the mouse take 3 seconds to reach the center of the turntable what torque does the mouse exert of the turntable? 11 6. A turntable with a moment of inertia of 5.4 x 10-3 kg ma r freely with an angular speed of 33.3 rpm. Riding the rim of the turntable, 15 cm from the center, is a 32-g mouse. a) If the mouse walks toward the center of the turntable, what is the angular speed of the mouse when is at half the distance to the center? b) If the mouse take 3 seconds to reach the center of the turntable what torque does the mouse exert of the turntable?Explanation / Answer
given I = 5.4*10^-3 kg m^2
w = 33.3 rpm = 33.3*2*pi/60 rad/s = 3.487 rad/s
r = 15 cm = 0.15 m
m = 32*10^-3 = 0.032 kg
a. at r/2
angular speed = w'
new moment of inertia = I'
from conservation of angular momentum
(I + mr^2)w = (I + mr^2/4)w'
w' = 36.52258 rpm
b. torque = change in angular momentum / time
time = 3 s
change in amgular momentum = I(w' - w) = 0.001822326
T = 6.07442-4 Nm
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