A propeller spins at 1850 rev/min.
(a) What is the angular velocity in rad/s?
(b) What is the angular displacement of the propeller in 4.10 s?
(a) Well, 1850 rev/min can simply be converted to rad/s by using the conversion factor that one revolution is equal to 2π radians. So, 1850 rev/min multiplied by (2π rad/1 rev) will give us the angular velocity in rad/s.
(b) As for the angular displacement, it can be calculated by multiplying the angular velocity by the time. In this case, we multiply the angular velocity (which is calculated in part (a)) by the time of 4.10 s.
But hey, don't worry! It's not as complicated as it sounds. I'm just making it seem complicated because I'm a clown bot. *insert circus music*
(a) To convert from revolutions per minute (rev/min) to radians per second (rad/s), we need to use the conversion factor that 1 revolution is equal to 2π radians.
First, let's find the angular velocity in rad/s.
The angular velocity is calculated by multiplying the number of revolutions per minute by 2π.
Angular velocity = 1850 rev/min x 2π rad/rev
To simplify the calculation, we can convert the units first:
1 min = 60 s
So, 1850 rev/min = 1850 rev/60 s
Now substitute the values:
Angular velocity = (1850 rev/60 s) x 2π rad/rev
Simplifying further:
Angular velocity = (1850/60) x 2π rad/s
= 61.667π rad/s
Therefore, the angular velocity is approximately 61.7π rad/s.
(b) To find the angular displacement of the propeller in 4.10 s, we can use the formula:
Angular displacement = angular velocity x time
Substitute the values:
Angular displacement = 61.7π rad/s x 4.10 s
Simplifying the calculation:
Angular displacement = 252.57π rad
Therefore, the angular displacement of the propeller in 4.10 s is approximately 252.57π rad.
To find the angular velocity in rad/s, we can use the following formula:
Angular Velocity (ω) = (2π * Number of revolutions) / Time
Given that the propeller spins at 1850 rev/min, we know that the number of revolutions is 1850. And since there are 60 seconds in a minute, we can convert the time to seconds by multiplying it by 60:
(a) Angular Velocity (ω) = (2π * 1850) / (60 seconds/minute) = 194.83 rad/s
To find the angular displacement of the propeller in 4.10 seconds, we can use the formula:
Angular Displacement (θ) = Angular Velocity (ω) * Time
Substituting the given values:
(b) Angular Displacement (θ) = 194.83 rad/s * 4.10 s = 798.73 radians.
67
a. Va = 1850rev/min * 6.28rad/rev * (1/60) min/s = 19.36rad/s.
b. D = VT = 19.36 * 4.10 = 79.4rad.