You are to design a rotating cylindrical axle to lift 800 N buckets of cement from the ground to a rooftop 78.0 m above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise. (a) What should the diameter of the axle be in order to raise the buckets at a steady 2.00 cm/s when it is turning at 7.5 rpm? (b) If instead the axle must give the buckets an upward acceleration of 0.400 m/s2, what should the angular acceleration of the axle be?

You are to design a rotating cylindrical axle to lift 800 N buckets of cement from the ground to a rooftop 78.0 m above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise. (a) What should the diameter of the axle be in order to raise the buckets at a steady 2.00 cm/s when it is turning at 7.5 rpm? (b) If instead the axle must give the buckets an upward acceleration of 0.400 m/s2, what should the angular acceleration of the axle be?

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A: Velocity (V)= 2cm/s turning at 7.5 rpm upward acceleration = 0.400m/s2

Question

You are to design a rotating cylindrical axle to lift 800 N buckets
of cement from the ground to a rooftop 78.0 m above the ground.
The buckets will be attached to a hook on the free end of a cable that
wraps around the rim of the axle; as the axle turns, the buckets will rise.
(a) What should the diameter of the axle be in order to raise the buckets
at a steady 2.00 cm/s when it is turning at 7.5 rpm? (b) If instead the
axle must give the buckets an upward acceleration of 0.400 m/s2, what
should the angular acceleration of the axle be?

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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