Please show work on each part.. thanks Part A: At time t=0 s, a wheel has an ang

Question

Please show work on each part.. thanks

Part A: At time t=0 s, a wheel has an angular displacement of zero radians and an angular velocity of +24 rad/s. The wheel has a constant acceleration of -0.49 rad/s^2. The time t at which the wheel comes to a halt is closest to

a) 100 s

b) 86 s

c) 49 s

d) 69 s

e) 120 s

Part B: A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time (neglect friction and assume the spring obeys Hooke

Explanation / Answer

A)

he initial angular displacement is irrelevant. For uniform angular acceleration, change in angular velocity is the angular acceleration multiplied by time:

?? = ?t
?_final - ?_initial = ?t

When the wheel comes to a stop, that means that ?_final is zero so our above equation becomes:
-?_initial = ?t

Dividing both sides by angular acceleration, ?:
-?_initial / ? = t

Plugging in our given values into the above equation:

-( 24 rad/sec ) / ( -0.49 rad/sec

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