Question

A wheel rotates from rest with constant angular acceleration. If it rotates through 8.00 revolutions in the first 2.50 s, how many more revolutions will it rotate through in the next 5.00 s?

Answer 1

Using 2nd rotational kinematic equation:

= wi*t + (1/2)**t^2

given that in t = 2.50 sec, = 8.00 rev = 8.00*2*pi rad,

wi = initial angular velocity = 0 rad/sec

So,

16.00*pi = 0*2.50 + (1/2)**2.50^2

= 2*16.00*pi/2.50^2 = 16.08 rad/sec^2

Now in t = 7.50 sec (next 5.00 sec) number of revolutions will be:

1 = 0*7.50 + (1/2)*16.08*7.50^2 = 452.25 rad

So revolutions will be:

1 = 452.25/(2*pi) = 72.0 rev

Since in t = 2.50 sec, 8.00 rev, So

in next 5.00 sec,

revolutions = 1 - = 72.0 - 8.00 = 64.0 rev

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