The initial angular speed of the fan will be 55.0 rad/sec. The angular speed of the fan decreases to 84.7 rad/s in 2.96 s.
<h3>What is angular acceleration?</h3>
Angular acceleration is defined as the pace of change of angular velocity with reference to time.
Given data;
Final angular speed,
Initial angular speed, 
Time period,t= 2.96 s
Angular deceleration = 47.2 rad/s²

Hence the initial angular speed of the fan will be 55.0 rad/sec.
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Acceleration occurs whenever the forces on an object are unbalanced.
It's the group of forces on the object that's either balanced or unbalanced.
There's no such thing as "an unbalanced force".
Answer:
The acceleration towards the center will be 
Explanation:
Given the running track is an oval shape, and the diameter of each half-circle is 74 meters.
Also, the runner took 1 minute and 40 seconds to complete 400 m one round of the track.
We need to find the acceleration towards the center.
First, we will find the speed.

Where
is the speed.
is the distance covered by the rider that is 400 meters.
is the time taken by the rider to complete the lap which is 1 minute and 40 seconds.
seconds.
So,

And

Where
is the acceleration towards the center.
is the radius which will be the half of the diameter 74 meters.
Hence, the radius will be 37 meters.

So, the centripetal acceleration of the rider will be 