Step 1: Find revolutions made by disk when speeding up
Using 1st rotational kinematic equation:
w1 = w0 + *t1
Given that disk starts from rest, So w0 = 0 rad/sec
w1 = 0 + *t1
= w1/t1 = angular acceleration of disk when speeding up
Now Using 2nd rotational kinematic equation:
= w0*t1 + (1/2)**t1^2
= 0*t1 + (1/2)*(w1/t1)*t1^2
= (w1*t1)/2
Step 2: Now find number of revolutions when it undergoes negative constant angular acceleration
Using 1st rotational kinematic equation:
w2 = w1 - *t2
Given that disk finally stops, So w2 = 0 rad/sec
0 = w1 - *t2
= w1/t2 = angular de-acceleration of disk when speeding down
Now Using 2nd rotational kinematic equation:
= w1*t2 - (1/2)**t2^2
= w1*t2 - (1/2)*(w1/t2)*t2^2
= (w1*t2)/2
So total angular displacement of disks will be:
= +
= (w1*t1)/2 + (w1*t2)/2
= w1*(t1 + t2)/2
Let me know if you've any query.
A disc, starting from rest, undergoes a constant angular acceleration for a time t_1 and reaches...
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