Question

A 53-cm-diameter wheel accelerates uniformly about its center from 110 rpm to 330 rpm in 4.6 s .

The angular acceleration is 5.0 rad/s²

A. Determine the radial component of the linear acceleration of a point on the edge of the wheel 1.4 s after it has started accelerating.

Express your answer to two significant figures and include the appropriate units.

B. Determine the tangential component of the linear acceleration of a point on the edge of the wheel 1.4 s after it has started accelerating.

Express your answer using two significant figures.

Answer 1

W, = 21Tf, = 2X3.148/110 60 W₂ = 217f2 = 2x3:14 X (330) = 34.54 rad/s 2 = 5 rad /s2 - angular accelesation constant B) We know that tangential acceleration is, Given: R=53810 m A) let, t = 1.45, ap=? Let, angular acceleration is constant, then angular relocity of wheel at given instant t=1.4s is, W = 60,+ K= 11.513 + 5x64 "W2 = 18.513 rad's Now, V=Rw = 53x102 x 18.513 oiv=9.8119 m/s We know that, radial acceleration is, v² (9.8119) 2 ar = R (538102) ap=181.65 m/s2 ap=1.8x10² m/s2 a = RX = 53x102x5 .at = 2.65 m/s2 ay= 2.6 m/s2