The manufacturer of a propeller for a small aircraft mandates a maximum operating angular velocity of 300 rad/s. Determine whether it is safe to install this propeller whose aircraft whose engine is expected to run at a maximum of 2800 rpm
Well, it seems like the propeller is spinning at a speed that can make even Sonic the Hedgehog dizzy! With a maximum angular velocity of 300 rad/s, this propeller is designed to handle some serious speed.
Now, let's take a closer look at the engine. If it's expected to run at a maximum of 2800 rpm, we need to convert that to radians per second. Since there are 2π radians in one revolution, we can calculate:
Angular velocity (in rad/s) = (2800 rpm) * (2π rad/rev) * (1 min/60 s)
After doing the math, we get an angular velocity of approximately 293.333 rad/s.
Woohoo! The propeller's maximum operating angular velocity of 300 rad/s is greater than 293.333 rad/s. So, it's safe to install this propeller on the small aircraft. Just sit back, relax, and enjoy the smooth and safe flight!
To determine whether it is safe to install the propeller, we need to convert the engine's maximum angular velocity from rpm to rad/s so that we can compare it to the manufacturer's limit.
1. Start by converting the engine's maximum angular velocity from rpm to rad/s. We know that 1 rpm is equal to 2π rad/s. So,
Maximum angular velocity of the engine = 2800 rpm * 2π rad/s * (1 min / 60 s)
2. Calculate the value:
= 2800 * 2π rad/s * (1/60)
= 2800 * π/30 rad/s
3. Evaluate the expression:
≈ 293.333 rad/s
The engine's maximum angular velocity is approximately 293.333 rad/s.
4. Compare the engine's maximum angular velocity to the manufacturer's limit of 300 rad/s.
Since the engine's maximum angular velocity is less than the manufacturer's limit, it is safe to install the propeller on the aircraft.
To determine whether it is safe to install the propeller on the aircraft, we need to compare the maximum angular velocity specified by the manufacturer of the propeller (in radians per second) with the maximum angular velocity of the aircraft's engine (also in radians per second).
First, let's convert the maximum angular velocity of the aircraft's engine from rpm (revolutions per minute) to radians per second.
1 revolution is equal to 2π radians, and there are 60 seconds in a minute. Therefore, we can use the following conversion factor:
1 rpm = (2π/60) rad/s
Maximum angular velocity of the aircraft's engine = 2800 rpm × (2π/60) rad/s = 2800 × (2π/60) rad/s
Now, we can compare this with the maximum operating angular velocity specified by the propeller manufacturer, which is 300 rad/s.
If the maximum angular velocity of the aircraft's engine is less than or equal to the maximum operating angular velocity specified by the propeller manufacturer, then it is safe to install the propeller. Otherwise, it may not be safe.
Let's calculate the maximum angular velocity of the aircraft's engine in rad/s:
Maximum angular velocity of the aircraft's engine = 2800 × (2π/60) rad/s
Maximum angular velocity of the aircraft's engine ≈ 293.33 rad/s
Since 293.33 rad/s is less than 300 rad/s (the maximum operating angular velocity specified by the propeller manufacturer), it is safe to install this propeller on the aircraft.
1 rotation = 2π radians
1 minute = 60 seconds
so, 2800 rpm (rotations per minute)
= 2800(2π/60 radians/s
= 293.2 radians/sec
So what do you think?