e Print Calculator Periodic Table Question 21 of 29 Map A motorized wheel is spi

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e Print Calculator Periodic Table Question 21 of 29 Map A motorized wheel is spinning with a rotational velocity of wb 1.41 rad/s. At t o s, the operator switches the wheel to a higher speed setting. The rotational velocity of the wheel at al subsequent times is given by uoft w atan br where c 1.5574 and b -6.97 s 2 At what time, Himax is the rotational acceleration a maximum? ti Number mS What is the maximum tangential acceleration, at, of a point on the wheel a distance R 1.17 m from its Center? Number What is the magnitude of the total acceleration of this point? Number Previous & Give Up s View Solution Check Answer O Next Exit Hint

Explanation / Answer

here,

w(t) = wo * arcTan(bt^2 + c)
w(t) = 1.41 * arcTan(6.97*t^2 + 1.5574)

Angular acceleration, alpha = dw/dt
alpha = (414*arcTan(6.97*t^2 + 1.5574))/100

alpha will be maximum when,

(arcTan(6.97*t^2 + 1.557))/100 = pi/4
(6.97*t^2 + 1.5574)= tan(pi/4)*100
(6.97*t^2 + 1.5574) = 100
t = 3.758 s

alpha = (414*arcTan(6.97*(3.758)^2 + 1.5574))/100
alpha = 370.228 rad/s^2

Since Tangential acceleration, at = alpha *r
at = 370.228 * 1.17
at = 433.167 m/s^2

Net magnitude of acceelration,
a = sqrt(at^2 + alpha^2)
a = sqrt(433.167^2 + 370.228^2)
a = 569.827 m/s^2

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