((QUESTION 1)) You wish to accelerate a small merry-go-round from rest to a rota

Question

((QUESTION 1))

You wish to accelerate a small merry-go-round from rest to a rotational speed of one-half of a revolution per second by pushing tangentially on it. Assume the merry-go-round is a disk with a mass of 250kg and a radius of 1.80m .

Part A

Ignoring friction, how hard do you have to push tangentially to accomplish this in 7.00s ? (Use energy methods and assume a constant push on your part.)

((QUESTION 2))

A hoop starts from rest at a height 2.0m above the base of an inclined plane and rolls down under the influence of gravity.

Part A

What is the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.)

Express your answer using two significant figures.

Explanation / Answer

alfa = W2-W1)/t = (0.5*2*3.14-0)/7 = rad/s^2

torque = I*alfa

F*R = 0.5*M*R^2*alfa

F = 0.5*M*R*alfa = 0.5*250*1.8*0.448 = 100.8 N

B) m*g*h = 0.5*m*V^2 + 0.5*I*w^2

m*g*h = 0.5*m*V^2 + 0.5*m*R^2*V^2/R^2

gh = v^2

V = sqrt(gh) = (9.8*2)^0.5 = 4.43 m/s

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