Any help ? This problem concerns a rotating wheel. In the interval between t = 0

Question

Any help ? This problem concerns a rotating wheel. In the interval between t = 0.000 s and t = 0.250 s. the wheel's angular velocity is steadily changing. At the beginning of the interval, the angular velocity is 5.37 rev/s (revolutions per second) in the counterclockwise direction, but by the end of the interval the angular velocity is 3.48 rev/s in the counterclockwise direction. Calculate the angular acceleration of the wheel during this interval. I am interested in the magnitude of this angular acceleration, so you don't have to sorry about the sign in this part. Specify your answer in units of radians/s^2. For parts b and c. 1 am interested in one specific instant within the interval described above, when the wheel has an angular velocity of 4.72 rev/s in the counterclockwise direction. At this particular instant, a small oil spot happens to be at the top of the wheel, as shown in the figure below. This spot is 0.406 m away from the axis of rotation, as shown. Calculate the translational velocity vector v of the oil spot at this instant. Specifically, give the x and y components of v using the x and y directions specified in the figure. These components should have units of m/s. Calculate the translational acceleration vector a of the oil spot at this instant. Specifically, give the x and y components of a using the x and y directions specified in the figure. These components should have units of m/s^2.

Explanation / Answer

a)

alpha = w2-w1/t2-t1

alpha = (3.48-5.37)2pi /0.25-0

alpha = 47.5 rad/s^2

b)

V = Vx i + Vy

Vy = 0

V = Wxr i + 0

V = 4.72x2pix0.406 i + 0

V = 12.0406 m/sec i + 0 j

c)

a = alpha x r i + 0 j

a = -19.285 m/sec^2 i + 0 j

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