A propeller spins at 1880 rev/min.
the equals 197 rads/sec
b. What is the angular displacement of the propeller in 2.50 s ?
If you have angular velocity and you need angular displacement, just remember:
velocity=displacement/time
so solve that for displacement and it's
displacement=velocity*time
so it should be
angular displacement=(197 rad/s)(2.5 s)
and your answer should be 492.5 rad, be careful of whether the answer is supposed to be in degrees or radians
Well, if the propeller spins at a rate of 1880 rev/min, that means it completes 1880 revolutions in one minute. Now, let's convert that to radians per second.
To convert from revolutions per minute to radians per second, we use the formula:
angular velocity in rad/sec = (2π * revs per min) / (60 sec/min)
Plugging in the values, we get:
angular velocity in rad/sec = (2π * 1880) / 60
Now, let's calculate it:
angular velocity in rad/sec ≈ 197 rads/sec (rounded to nearest whole number)
So, it seems you've already done part a and obtained an angular velocity of 197 rads/sec. Great job!
Now, for part b, we need to find the angular displacement of the propeller in 2.50 seconds. To do this, we use the formula:
angular displacement = angular velocity * time
Plugging in the values, we get:
angular displacement = 197 * 2.50
Calculating it:
angular displacement ≈ 492.5 radians
Therefore, the angular displacement of the propeller in 2.50 seconds is approximately 492.5 radians. That's a lot of spinning!
To find the angular displacement of the propeller, we can use the formula:
Angular displacement = angular velocity × time
Given:
Angular velocity (ω) = 197 rad/sec
Time (t) = 2.50 s
Substituting the values into the formula, we have:
Angular displacement = 197 rad/sec × 2.50 s
Calculating this expression, we get:
Angular displacement = 492.5 rad
Therefore, the angular displacement of the propeller in 2.50 s is 492.5 radians.
To find the angular displacement of the propeller in 2.50 s, we need two pieces of information: the angular velocity of the propeller in radians per second and the time interval.
We are given that the angular velocity (ω) of the propeller is 197 radians per second (rads/sec).
So, to calculate the angular displacement (θ) in 2.50 seconds, we can use the formula:
θ = ω * t
where ω is the angular velocity and t is the time interval.
Plugging in the values, we have:
θ = 197 rads/sec * 2.50 s = 492.5 radians.
Therefore, the angular displacement of the propeller in 2.50 seconds is 492.5 radians.