A flywheel with an outside radius of 0.4 meters rotates about a central fixed ax

Question

A flywheel with an outside radius of 0.4 meters rotates about a central fixed axis. It's angular displacement is given by the relationship: ? = 4t2 - 3t + 2, where ? is measured in radians and t is in seconds.

A) What is the initial angular displacement of the wheel?

B) What is the angular displacement of the wheel in question 1 at t = 2.0 s?

C) What is the angular velocity of the wheel in question 1 at t = 2.0 s?

D) Flywhat is the angular acceleration of the wheel in question 1 at t = 2.0 s?

E) What is the tangential acceleration at 2.0 s on the outside rim of the wheel described in question 1?

F) What is the centripetal acceleration at 2.0 s on the outside rim of the wheel described in question 1?

G) What is the total acceleration at 2.0 s on the outside rim of the wheel described in question 1?

Explanation / Answer

A) initial angular displacecent = theeta(0) = 2 radians

B) at t = 2 ..

angular displacement = theeta(2) = 4*2^2 - 3*2 + 2 = 12 radians

C) andular velocity = d theeta / dt = 8t - 3 = 8*2 - 3 = 13 rad/sec

D) angular acceleion = d(angular vel) / dt = 8 rad/sec2

E) angentaial acc = angular ac * radius = 8*0.4 = 3.2 m/sec2

F)

tangential velo = angular vel * rad = 13*0.4 = 5.2 m/sec

so. centipetal acc = tangentaial vel^2 / rad = 5.2^2 / 0.4 = 67.6 m/sec2

G) total acc = sqt ( tangentaial^2 + centripetal^2 ) = 67.675697 m/sec2

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