Final answer:
The body makes a total of 200 rotations while accelerating from 600rpm to 1800rpm over 10 seconds, using the kinematic equations for rotational motion.
Step-by-step explanation:
A body rotating with an initial angular speed of 600rpm is uniformly accelerated to an angular speed of 1800rpm over a period of 10 seconds. To find the total number of rotations made by the body in this process, we'll first convert the angular speeds from rpm to revolutions per second (rps) and then use the formula for angular motion:
Initial angular speed (ω0) = 600rpm = 10rps (since 1rpm = 1/60rps)
Final angular speed (ω) = 1800rpm = 30rps
Time (t) = 10s
The angular acceleration (α) can be calculated using the formula:
α = (ω - ω0) / t
Let's calculate the angular acceleration:
α = (30rps - 10rps) / 10s = 2rps²
To find the number of rotations, we use the formula for the total angle (θ in revolutions) turned in time t under constant angular acceleration:
θ = ω0*t + (1/2)*α*t²
θ = 10 rotations/second * 10 seconds + (1/2)*2 rotations/second² * (10 seconds)²
θ = 100 + 100 = 200 rotations
The body makes a total of 200 rotations in the process of accelerating from 600rpm to 1800rpm over 10 seconds.