Step-by-step explanation:
it is not necessary to know for this question, but FYI
1 rad = 180/pi = 57.29577951...°
in essence it describes the arc angle of the arc with the length = radius.
anyway,
we are only dealing with relative sizes here all expressed in radians.
the original spin rate or angular velocity is 5.0 rad/sec.
that means in 1 second it spins by 5 radians (a point on the surface moves by that many degrees).
remember, acceleration is speed/time or distance/time².
then we measure again - after the ball moved by a total angle of 5.5 radians. so, it was longer than 1 second.
so, how much time passed ?
time = distance / speed
5.5 rad / 5.0 rad /1 sec = 1 sec × 5.5 rad / 1×5.0 rad =
= 5.5 sec / 5.0 = 1.1 sec
so, the acceleration was
1.5 - 5.0 = -3.5 rad/(1.1 sec)² = -3.5 rad / 1.21 sec² =
= -2.892561983... rad/sec²