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HSC Stuff => HSC Science Stuff => HSC Subjects + Help => HSC Physics => Topic started by: erucibon on November 05, 2019, 02:10:05 pm

Title: (Circ Motion) acceleration methods
Post by: erucibon on November 05, 2019, 02:10:05 pm: Why does using a vector diagram and the centripetal acceleration formula give different values? (using exact values in both so it isn't rounding errors)
A mass lies on a perfectly smooth horizontal surface and is connected to a 1.2m string. The mass completes 5 rotations per second. Position B differs from Position A by 60 degrees.

Calculating the acceleration using the centripetal acceleration formula with 5 rotations per second as the speed gives 1184ms-2. By calculating the time it takes to move to B (0.033s, exact value is used in acceleration calculation), and then drawing a vector diagram to find change in velocity and then finding acceleration through change in velocity over time, I get 1131ms-2 (using exact values).

$a_c = \frac{(5\times1.2\times2\pi)^2}{1.2}$

$a=\frac{5\times1.2\times2\pi}{\frac{\frac{60}{360}\times2\pi\times1.2}{5\times1.2\times2\pi}}$

Shouldn't the magnitude of centripetal acceleration be the same regardless of whether it is moving from one point to another?

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