1.(a)A centrifuge accelerates from rest with an angular acceleration of 30rad/s^2.What is the angular velocity of the centrifuge after 30s?(b)The angular velocity of an auto mobile engine accelerates from 800rpm to 3000rpm in 15s.calaculate the engines angular acceleration.
Angualar velocity final=intial w + angular acceleration* time
In the second part, change rpm to radians/sec^2
A 200kg satellite is circling the earth in an orbit of radius 7.0x10^6 m in radius. At this radius the acceleration due to gravity is 8.2 m/s2. The speed of the satellite is?
vaegina
To find the angular velocity of the centrifuge after 30 seconds, we can use the formula:
Angular velocity final = initial angular velocity + angular acceleration × time
Given:
Initial angular velocity (ω0) = 0 (as it starts from rest)
Angular acceleration (α) = 30 rad/s^2
Time (t) = 30 s
Plugging in the values, we have:
Angular velocity final = 0 + 30 × 30
Angular velocity final = 900 rad/s
Therefore, the angular velocity of the centrifuge after 30 seconds is 900 rad/s.
Now, let's move on to the second part of the question.
To calculate the engine's angular acceleration, we can use the formula:
Angular acceleration = (final angular velocity - initial angular velocity) / time
Given:
Initial angular velocity (ω0) = 800 rpm
Final angular velocity (ωf) = 3000 rpm
Time (t) = 15 s
First, we need to convert the angular velocities from revolutions per minute (rpm) to radians per second (rad/s).
Since 1 revolution is equal to 2π radians, we can use the conversion factor:
1 rpm = 2π/60 rad/s
Converting the initial angular velocity:
Initial angular velocity (ω0) = 800 rpm × 2π/60 rad/s
Initial angular velocity (ω0) = 83.78 rad/s
Converting the final angular velocity:
Final angular velocity (ωf) = 3000 rpm × 2π/60 rad/s
Final angular velocity (ωf) = 314.16 rad/s
Now, we can calculate the angular acceleration:
Angular acceleration = (314.16 rad/s - 83.78 rad/s) / 15 s
Angular acceleration = 230.38 rad/s^2
Therefore, the engine's angular acceleration is 230.38 rad/s^2.