The angular velocity of a gear is controlled according to ω = 79 − 5t2 where ω, in radians per second, is positive in the clockwise sense and where t is the time in seconds. Find the net angular displacement Δθ (poisitive in the clockwise sense) from the time t = 0 to t = 4 s. Also find the total number of revolutions N through which the gear turns during the 4 seconds.

is the angular displacement in 4 seconds.

Explanation:

Given:

time of observation,

angular velocity as a function of time,

where:

angular velocity

time taken

Now for the angular displacement we integrate the expression of angular velocity:

is the angular displacement in 4 seconds.

Now the no. of revolutions made during this time;

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