Answer to Question #109145 in Mechanics | Relativity for Sagaru

Question #109145
A wheel 2.0 m in diameter lies in the vertical plane and rotates about its central axis
2
Take g  10ms
.
with a constant angular acceleration of 4.0rads
t  0 and the radius vector of a point A on the wheel makes an angle of 60o with the
. The wheel starts from rest at horizontal at this instant. Calculate the angular speed of the wheel, the angular
1
Expert's answer
2020-04-15T10:12:14-0400

More correctly


A wheel "2 .0" m in diameter lies in the vertical plane and rotates about its central axis with a constant angular acceleration of "4.0" "rad\/s^2". The wheel starts from rest at "t=0" and the radius vector of a point A on the wheel makes an angle of "60\u00b0" with the horizontal at this instant. Calculate the angular speed of the wheel, the angular position of the point A and the total acceleration at "t=2.0" s.


The angular speed of the wheel


"\\omega=\\omega_0+\\epsilon t=0+4\\cdot2=8rad\/s"


The angular position of the point A


"\\phi=\\phi_0+\\omega_0t+\\frac{\\epsilon t^2}{2}=\\pi\/3+0+\\frac{4\\cdot2^2}{2}=9.047rad"


"9.047-2\\cdot3.14159=2.764rad" or "\\approx158\u00b0" with the horizontal.


The total acceleration


"a=\\sqrt{(\\omega^2R^2)^2+\\epsilon^2R^2}=\\sqrt{(8^2\\cdot 1^2)^2+4^2\\cdot 1^2}=64.1m\/s^2"








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