Question

# a) At a certain instant, a rotating turbine wheel of radius R has angular speed ω...

a) At a certain instant, a rotating turbine wheel of radius R has angular speed ω (measured in rad/s). What must be the magnitude α of its angular acceleration (measured in rad/s2) at this instant if the acceleration vector a⃗ of a point on the rim of the wheel makes an angle of exactly 30∘ with the velocity vector v⃗ of that point? Express your answer in terms of some or all of the variables R and ω.

b) At this same instant, what is the angle between a⃗  and v⃗  for a point on the wheel halfway between the axis of rotation and the rim?

c) A flywheel with radius of 0.200 m starts from rest and accelerates with a constant angular acceleration of 0.400 rad/s^2, tangential acceleration is 8.00 x 10^-2 m/s^2. What is the magnitude of radial acceleration and the resultant acceleration after 2 seconds?

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