Use 3-sig figs. and g 9.8 m/s^2 A thin circular wheel (radius 3.00 m) rotates ab

Question

Use 3-sig figs. and g 9.8 m/s^2 A thin circular wheel (radius 3.00 m) rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0 s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0 s interval. I low many radians does the wheel turn through during the 5.0 s interval? A particle of mass 4.5 kg that is initially moving along a x-axis with speed 3.0 m s. Determine the average force applied on the particle to give it a new velocity of(-8.1i + 13.0j) m/s in 0.55s.

Explanation / Answer

1. wi= 20rad/s , wf = 10rad/s , t = 5s

= (wf - wi)/ t = (10-20)/5 = -10/5 = -2rad/s^2

To find use equation,

wf^^2 = wi^2 +2**

10^2 = 20^2 -2*2*      =>    = 75rad

2.

Fnet= p/t = m(vf-vi)/t  = 4.5[(-8.1i + 13.0j) - (3i +0j)]/0.55 = 4.5[(-11.1i -13j)]/0.55 = (-90.82i - 106.36j)

|Fnet| = sqrt(90.82^2 +106.36^2) = 139.86 N

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