Recent content by ac7597

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    Complex numbers: convert the exponential to polar form

    Yes j=√-1
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    Complex numbers: convert the exponential to polar form

    Yes, the question is rather 4e^(-1*j) = 4 ∠-180° ?
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    Complex numbers: convert the exponential to polar form

    Summary:: Hello, my question asks if the complex exponential equation 4e^(-j) is equal to 4 ∠-180°. I tried to use polar/rectangular conversions: a+bj=c∠θ with c=(√a^2 +b^2) and θ=tan^(-1)[b/a] 4e^(-j)=4 ∠-180° c=4, 4=(√a^2 +b^2) solving for a : a=(√16-b^2) θ=tan^(-1)[b/a]= -1 b/(√16-b^2)=...
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    Troubleshooting Wave Velocity on a Piano Wire

    angular frequency= 50 rad/s= 2*pi*frequency frequency= 7.96 Hz k=2*pi/wavelength k=2*pi/(2*1.6m) = 1.96 velocity=angular frequency/ k velocity=50/ 1.96 = 25.5 m/s For some reason this velocity is wrong
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    How Do You Calculate the Tension of a Cello String?

    wavelength of string= 2*L wavelength of string=2*0.70m= 1.4m velocity of string= frequency * wavelength velocity of string= 220Hz * 1.4m= 308 m/s tension= (308m/s)^2 * 0.00196 kg/m =186N Is the tension correct?
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    Harmonic motion of four meter sticks

    (4*0.1*9.8*0.707/0.33)^1/2 = 2pi/period period=2.17 seconds That's correct
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    Harmonic motion of four meter sticks

    inertia of center = [(1/12) m*L^2 + m(L/2)^2]*4 inertia of center = (4m*L^2)/ 3 inertia around pin = (4m*L^2)/ 3 + 4m(L/ 2^(1/2) )^2 inertia around pin = (10m*L^2)/ 3 inertia around pin = (10*0.1*1^2)/ 3 = 0.33 kg*m^2 d= 1/2^(1/2) = 0.707m (m*g*d/inertia)^1/2 = 2pi/period...
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    Kinematics without rolling or sliding

    I initially thought it is v, because the speed shouldn't change when the tape is on top.
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    How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

    linear distance = radians * radius 0.65m= radians * 0.01m radians= 65 rad thus with kinematics: 65rad= (1/2) (25.6) *time^2 time=2.25 seconds
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    How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

    90degrees
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    How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

    sorry about the mistake. total moment of inertia= 2.03*10^(-3) kgm^2 torque= 5.2 * 0.01 = 5.2 E-2 angular acceleration = (5.2 E-2)/ (2.03E-3)= 25.6 rad/s^2 I don't know how to solve for the time.
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    How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

    Is the torque just involves the cylindrical spindle thus : torque= (1/2) (0.016kg) (0.01m)^2 ?
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    Engineering BJT circuit with cascaded stages

    This cascade is divided into 3 sections thus: the leftmost section is an emitter follower : Ib1 = (15V-0.7V)/ ( R1 + 151R2) IE1= 151*Ib1 re1= 26mV /(IE1) Zb1= 150( re1+ R2) AV1= (-150*R1)/ (R1+Zb1) the center section is an unbiassed BJT : Ib2 = (15V-0.7V)/ ( R3 + 151(R4+Re2a) ) IE2=...
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    How Accurate Is the Calculation of Angular Acceleration and Time for a Yo-yo?

    total moment of inertia= (1/2) (0.098kg) ( 0.144m)^2 + (1/2) (0.098kg) ( 0.144m)^2 + (1/2) (0.016kg) (0.01m)^2 total moment of inertia= 2.03*10^(-3) kgm^2 torque= 5.2N * (0.144m) = 0.75N*m thus: 0.75N*m= 2.03*10^(-3) kgm^2 * angular acceleration angular acceleration = 368.8 rad/s^2 Is...
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    How Does Torque Affect Angular Acceleration in a Circular Disk?

    Is it -1.32N*m?