A size-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 6.50 m above the base of the hill. We can model this ball as a thin-walled hollow sphere.

a) At what rate was it rotating at the base of the hill?

b) How much rotational kinetic energy did it then have?

a) At what rate was it rotating at the base of the hill?

b) How much rotational kinetic energy did it then have?

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A thin, rectangular sheet of metal has mass M and sides of length a and b. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet.

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If we multiply all design dimensions of an object by a scaling factor f, its volume and mass will be multiplied by f^{3}.

a) By what factor will its moment of inertia be multiplied?

b) If a (1/48)-scale model has a rotational kinetic energy of 2.5 J, what will be the kinetic energy for the full-scale object of the same material rotating at the same angular velocity?

a) By what factor will its moment of inertia be multiplied?

b) If a (1/48)-scale model has a rotational kinetic energy of 2.5 J, what will be the kinetic energy for the full-scale object of the same material rotating at the same angular velocity?

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A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to θ(t)= γt+ βt^{3}, where γ = 0.406 rad/s and β = 1.30×10^{−2} rad/s^{3}.

a) Calculate the angular velocity of the merry-go-round as a function of time.

b) What is the initial value of the angular velocity?

c) Calculate the instantaneous value of the angular velocity ω_{z} at t = 5.05 s .

d) Calculate the average angular velocity ω_{av - z} for the time interval t = 0 to t = 5.05 s .

a) Calculate the angular velocity of the merry-go-round as a function of time.

b) What is the initial value of the angular velocity?

c) Calculate the instantaneous value of the angular velocity ω

d) Calculate the average angular velocity ω

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The flywheel of a gasoline engine is required to give up 600 J of kinetic energy while its angular velocity decreases from 780 rev/min to 510 rev/min. What moment of inertia is required?

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