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At a certain instant a rigid wheel is spinning about its center of mass with angular velocity of magnitude ω and angular acceleration of mag
Question
At a certain instant a rigid wheel is spinning about its center of mass with angular velocity of magnitude ω and angular acceleration of magnitude α. Consider a point a distance r from the axis of rotation. What would be the magnitude of the acceleration of this point on the wheel?
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Physics
5 years
2021-08-28T19:10:51+00:00
2021-08-28T19:10:51+00:00 1 Answers
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Answers ( )
Answer:
a = r√(w⁴ + (alpha)²)
Explanation:
let w be the magnitude of angular velocity
r = radius
v = velocity = wr
angular acceleration, ā = v²/r = (wr)²/r = w²r
Also,
â = dv/dt = rdw/dt
given : alpha = dw/dt
hence, â = (alpha)r
the resultant acceleration, a, by Pythagoras is given as
a = √( â² + ā²) = √(r²w⁴ + r²(alpha)²)
simplifying,
a = √r²(w⁴ + (alpha)²)
a = r√(w⁴ + (alpha)²)