A flywheel of a radius .5 m starts from rest and under goes a uniform angular acceleration of 3 rad/sec2 for a period of 5 seconds. Find the angular velocity of the flywheel at the end of this time? Find the angular displacement (in radians) that the wheel turns through during this time?

ω=ε•t =3•5 = 15 rad/s

φ = ε•t²/2 = 3•25/2 = 37.5 rad

To find the angular velocity of the flywheel at the end of the given time, we can use the formula:

Angular velocity (ω) = Initial angular velocity (ω0) + Angular acceleration (α) * Time (t)

Here, the initial angular velocity (ω0) is 0 as the flywheel starts from rest, the angular acceleration (α) is given as 3 rad/sec^2, and the time (t) is given as 5 seconds.

So, we can substitute these values into the formula:

Angular velocity (ω) = 0 + 3 rad/sec^2 * 5 sec
= 15 rad/sec

Therefore, the angular velocity of the flywheel at the end of 5 seconds is 15 rad/sec.

To find the angular displacement of the flywheel during this time, we can use the formula:

Angular displacement (θ) = Initial angular velocity (ω0) * Time (t) + 1/2 * Angular acceleration (α) * Time^2 (t^2)

Again, substituting the given values into the formula:

Angular displacement (θ) = 0 * 5 sec + 1/2 * 3 rad/sec^2 * (5 sec)^2
= 0 + 1/2 * 3 rad/sec^2 * 25 sec^2
= 1/2 * 3 * 25 rad
= 37.5 rad

Therefore, the angular displacement of the flywheel during this 5-second period is 37.5 radians.