a propeller turns at 300 rpm. Find the angular speed in rad/sec and the linear speed at the tip if the tip to the center is 30cm

angular velocity = 300(2π) radians/minute

= 300(2π)/60 radians/sec
= 10π radians/sec

circumference = 2π(30) = 60π cm

so the linear velocity at the tip is 300(60π) cm/min
= 300(60π)/60 cm/se
= 300π cm/sec
or
3π m/sec

Well, let's see what we're spinning here. A propeller, huh? That sounds like a real twisty situation!

To find the angular speed in rad/sec, we need to convert the revolutions per minute to radians per second. Luckily, we have a handy conversion factor for that. One revolution equals 2π radians. So, to convert 300 rpm to rad/sec, we can do:

Angular speed (rad/sec) = 300 rpm * 2π rad/1 rev * 1 min/60 sec

Now, let's do a little math.

Angular speed (rad/sec) = 300 * 2π /60

And when you crunch those numbers, you'll find that the angular speed is approximately 31.42 rad/sec.

Now, onto the linear speed at the tip! The linear speed will be equal to the distance traveled per unit of time. In this case, it's the distance from the center to the tip, which is 30 cm.

Linear speed (cm/sec) = Angular speed (rad/sec) * Radius (cm)

But hold on a second! We want the linear speed in meters, not centimeters, because the SI system is all about going metric. So let's convert that 30 cm to meters, which is 0.3 meters.

Now we can plug in the numbers and calculate the linear speed:

Linear speed (m/sec) = 31.42 rad/sec * 0.3 m

And when we multiply those numbers together, *drumroll please*, we get a linear speed of approximately 9.426 m/sec.

So, there you have it! The angular speed is around 31.42 rad/sec and the linear speed at the tip is about 9.426 m/sec. Keep on spinning, propeller!

To find the angular speed of the propeller in radians per second, we need to convert the given value of revolutions per minute (rpm) to radians per second.

1 revolution = 2π radians
1 minute = 60 seconds

Therefore, to convert from rpm to radians per second, we can use the following conversion factor:
1 rpm = (2π radians / 1 revolution) * (1 revolution / 1 minute) * (1 minute / 60 seconds)
= π/30 radians/second

Given that the propeller turns at 300 rpm, we can calculate the angular speed in radians per second:

Angular speed = 300 rpm * (π/30 radians/second)
= 10π radians/second
≈ 31.4 radians/second

To find the linear speed at the tip of the propeller, we need to know the radius from the center to the tip. In this case, it is given as 30 cm.

The linear speed (v) at the tip of the propeller can be found using the formula:

Linear speed (v) = Angular speed (ω) * Radius (r)

Given ω = 31.4 radians/second and r = 30 cm = 0.3 meters

Linear speed (v) = 31.4 radians/second * 0.3 meters
= 9.42 meters/second

Therefore, the angular speed of the propeller is approximately 31.4 radians/second, and the linear speed at the tip is approximately 9.42 meters/second.

To find the angular speed in rad/sec, we need to convert the given RPM (revolutions per minute) to rad/s. The conversion factor between RPM and rad/s is as follows:

1 revolution = 2π radians

1 minute = 60 seconds

Therefore, to convert RPM to rad/s, we multiply the given value by 2π/60:

Angular speed in rad/sec = (300 RPM) * (2π/60) = 10π rad/s

Now let's find the linear speed at the tip of the propeller. The linear speed can be calculated using the formula:

Linear speed = angular speed * distance from the center

Given that the tip to the center is 30 cm, we first need to convert it to meters (since the angular speed is in rad/s):

Distance from the center = 30 cm = 0.30 m

Linear speed at the tip = (10π rad/s) * (0.30 m) = 3π m/s

So, the angular speed of the propeller is 10π rad/s, and the linear speed at the tip is 3π m/s.