physics you are on a merry-go-round and are a distance 4m from the axis of rotat
ID: 1311949 • Letter: P
Question
physics
you are on a merry-go-round and are a distance 4m from the axis of rotation . the merry-go-round start from rest and accelerates at an angular acceleration of 0.4rad/s2 for 4 seconds .it then rotates at a constant anglar velocity for 10 seconds , and then decelerates at a constant angular acceleration for 6 seconds when it again comes to rest . hint this problem has three phase , each of which is at constant angular acceleration.
A. what is your angular velocity at 4 seconds ?
B. what is your angular acceleration which slows you down to rest ?
C. How far, in meters, did you travel ?
Explanation / Answer
Angular Velocity
Angular velocity can be expressed as (angular velocity = constant):
? = ? / t (2a)
where
?= angular velocity (rad/s)
? = angular displacement (rad)
t = time (s)
Angular velocity can also be expressed as (angular acceleration = constant):
? = ?o + ? t (2b)
where
?o = angular velocity at time zero (rad/s)
? = angular acceleration (rad/s2)
Angular Displacement
Angular displacement can be expressed as (angular acceleration is constant):
? = ?o t + 1/2 ? t2 (2c)
Combining 2a and 2c:
? = (?o2 + 2 ? ?)1/2
Angular Acceleration
Angular acceleration can be expressed as:
? = d? / dt = d2? / dt2 (2d)
where
d? = change of angular displacement (rad)
dt = change in time (s)
so now coming to your problem,
A. use ? = ?o + ? t
=? t = 0.4radx4= 1.6 rad/s
B. here
?= 0
so alpha= - 1.6/6 =0.2667 rad/s
C. for the first part
? = + 1/2 ? t2 = 3.2 rad
in second part
? = ?o t =1.6x10 =16 rad
in third part
? = ?o t -1/2 ? t2 =4,7994 rad
so total distance= 23.994 rad
distance = rx theta= 95.976m
?o =1.6 rad/s
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