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Romashka-Z-Leto [24]
3 years ago
8

The angular velocity of a gear is controlled according to ω = 79 − 5t2 where ω, in radians per second, is positive in the clockw

ise 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.
Physics
1 answer:
mariarad [96]3 years ago
8 0

Answer:

\theta=209.33\ rad=11993.92^{\circ} is the angular displacement in 4 seconds.

N\approx33.32\ revolutions

Explanation:

Given:

time of observation, t=4\ s

angular velocity as a function of time, \omega=79-5t^2

where:

\omega= angular velocity

t= time taken

<u>Now for the angular displacement we integrate the expression of angular velocity:</u>

\theta=\int^{4}_{0} (79-5t^2)dt

\theta=[79t-\frac{5}{3} t^3]^{4}_{0}

\theta=209.33\ rad=11993.92^{\circ} is the angular displacement in 4 seconds.

<u>Now the no. of revolutions made during this time;</u>

N=\frac{\theta^{\circ}}{360^{\circ}}

N=\frac{11993.92^{\circ}}{360^{\circ}}

N\approx33.32\ revolutions

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