Question

A 75 cm diameter wheel accelerates uniformly about its center from 110 rpm to 280 rpm in 3.4 s. Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.7 s after it has started accelerating. Determine the tangential component of the linear acceleration of a point on the edge of the wheel 1.7 after it has started accelerating.

Answer 1

ω = ω0 + α t

α = (ω - ω0) / t = (280 - 110) / 3.4 = 50 rpm / sec

ω = 110 + 50 * 1.7 = 195 rpm after 1.7 sec

ω = 195 rpm / 60 = 3.25 rev / sec

v T = ω R = 3.25 rev / sec * .75 m = 2.44 m/sec tangential speed

aT = α R = 50 rpm / sec * .75 m = 37.5 rpm / sec = .625 m / sec^2

αR = ω^2 / R radial accelertion

out of time - just apply the basic equations as shown