Answer on Mechanics | Relativity Question for Gabe
w = 79 rev/min* (2 pi rad/rev) * (1 min/60s) = 8.27 rad/s
Divide that final angular velocity by 4 seconds to obtain the angular acceleration. Call that number "alpha"
alpha = (8.27 rad/s)/4.0s = 2.07 rad/s^2
The tangential acceleration of the bug
while the disk is speeding up is
a_t = alpha*R
where R = 4.5 in/39.37 in/meter = 0.1143 m. Therefore
a_t = 0.236 m/s^2
b) The tangential velocity at full speed is v_t = R*w
c) same tangential acceleration as (a)
centripetal acceleration @ t=1 s is
a_c (@ t=1) = R w^2,
where w is 1/4 of the value calculated in (a), since you are only 1/4 way through the acceleration interval.
For the total acceleration at t=1 s, use
a = sqrt[a_t^2 + a_c^2]
The tangent of the total acceleration vector relative to tangential direction is (a_c)/(a_t).
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