a particle moves uniformly around the circumference of a circle whose radius is 8 cm with a period of pi/20 s. the angular velocity w of the particle is
a. 2.5 rad/s
b. 3.2 X 10^2 rad/s
c. 40 rad/s
d. 7.9 rad/s
e. 96 rad/s
please explain
thanks!
i didn't get that....
frequency=1/Period
Well, let's start with the basics. The angular velocity, denoted by the Greek letter omega (ω), is a measure of how quickly an object rotates or moves in a circular path. Mathematically, angular velocity is defined as the change in angle per unit time.
In this case, we are given that the particle moves uniformly around the circumference of a circle with a radius of 8 cm. The period, which is the time it takes for the particle to complete one full revolution, is given as π/20 s.
To find the angular velocity, we need to calculate the angle traveled by the particle in one period. Since the particle moves uniformly, we can calculate the angle using the formula:
θ = (2πr) / d
Where θ is the angle traveled, r is the radius, and d is the distance traveled (in this case, the circumference of the circle).
In this case, the radius (r) is 8 cm, and the distance traveled (d) is the circumference of the circle, which is 2πr.
Substituting the values into the formula, we get:
θ = (2π * 8) / (2π * 8)
θ = 1 radian
Since the particle takes π/20 seconds to travel 1 radian, we can calculate the angular velocity as:
ω = θ / t
ω = 1 / (π/20)
ω = 20/π rad/s
Now, let's simplify the answer choices:
a. 2.5 rad/s - Nope, not close to 20/π.
b. 3.2 x 10^2 rad/s - Wow, that's way off!
c. 40 rad/s - Nope, not close to 20/π either.
d. 7.9 rad/s - Not quite there.
e. 96 rad/s - Nope, that's not it.
So, after going through the answer choices, we don't have a match. It seems like the correct answer is missing. Maybe the options were meant to include 20/π rad/s as a choice?
I hope this explanation was helpful, even though we couldn't find a matching answer choice. If you have any other questions, feel free to ask!
To find the angular velocity (ω) of the particle, we can use the formula:
ω = 2π/ T
where ω is the angular velocity in radians per second, and T is the period (time taken to complete one full revolution) in seconds.
Given that the period (T) is π/20 s, we can substitute this value into the formula:
ω = 2π / (π/20)
ω = 2π * (20/π)
ω = 40 rad/s
Therefore, the correct answer is option c. 40 rad/s.
Period is the reciprocal of frequency.
angular frequency is 2PI*frequency