metecture checkpoint Romewor raoncwork i Homework: Rotational Dynamics ll Deadli

Question

metecture checkpoint Romewor raoncwork i Homework: Rotational Dynamics ll Deadline: 100% until Monday, April 17 at 10:00 Flywheel with Weight A string is wrapped around a 15 kg metal flywheel. The flywheel has a radius of o,28 meters and has all its mass around its very outer rim. A weight with mass m 3.2 kg is attached to loose end of the string. when the 3.2 kg weight is dropping with a speed of 2.2 m/s, what the angular velodty of the fiyheen rad sec 2) when the weight is moving with a speed of 2.2 m/s, what the kinetic energy of the entire system the weight fallen? 1) the system started from rest, how far has 4) Through what ang e has the disk turned? radians 3) what is the anputar acceleration at ths pone do e Disk wit Ball on R Loop the

Explanation / Answer

(1) v= w r

w = 2.2 / 0.28 = 7.86 rad/s

(2) of mass, K1 =m v^2 /2

K1 = 3.2 x 2.2^2 /2 = 7.74 J

of flywheel, K2 = I w^2 / 2

= (15 x 0.28^2) (7.86^2)/2

= 36.32

total KE = K1 + K2 = 44.1 J

(3) total KE= m g h

44.1 = 3.2 x 9.8 x h

h = 1.41 m

(4) theta = h / r = 1.41 / 0.28

= 5.02 rad

(5) wf^2 - wi^2 = 2 alpha theta

7.86^2 - 0^2 = 2 (alpha) (5.02)

alpha = 6.16 rad/s^2

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