If an object moves in uniform circular motion in a circle of radius R = 1.0 meter, and the object takes 4.0 seconds to complete
ten revolutions, calculate the magnitude of the velocity around the circle. (Note: Remember, 10 revolutions is a counting number and not a measurement.)
2 answers:
Let's supose that your object is the orange rectangle rotating around the blue circle (see picture attached)
r = 1.0 [m] is the radius of the circle (it's R in your problem).
ω [rad/s] - is the angular velocity of the object, it is measured in radians per second. We will compute it from the data you have
v [m/s] - is the tangential/linear speed, it is measured in meters per second
We know that the rotational speed is 10 revolutions per 4 seconds.
10/4 rev/s = 2.5 rev/s
We convert rev/s in rad/s and we get:
2.5 rev/s = 15.708 rad/s
So we found our angular speed: ω = 15.708 rad/s
The relationship between v and ω is:
v = ω · r = 15.708 · 1 = 15.708 m/s
Answer: the magnitude of the velocity around the circle is 15.708 m/s
r = 1.0 [m] is the radius of the circle (it's R in your problem).
ω [rad/s] - is the angular velocity of the object, it is measured in radians per second. We will compute it from the data you have
v [m/s] - is the tangential/linear speed, it is measured in meters per second
We know that the rotational speed is 10 revolutions per 4 seconds.
10/4 rev/s = 2.5 rev/s
We convert rev/s in rad/s and we get:
2.5 rev/s = 15.708 rad/s
So we found our angular speed: ω = 15.708 rad/s
The relationship between v and ω is:
v = ω · r = 15.708 · 1 = 15.708 m/s
Answer: the magnitude of the velocity around the circle is 15.708 m/s
You might be interested in