Respuesta :
Answer:
5.09 cm
Explanation:
using the formula
V = rω where r is radius and ω is the angular speed and V is the speed
ω = 7. 5 rpm = 7.5 × 2πrad / 60 seconds = 0.7855 rad s⁻¹ since one revolution = 2π and 1 minutes = 60 seconds
2.00 cm/s =r ×0.7855 rad s⁻¹
r = 2.00 cm/s / 0.7855 rad s⁻¹ = 2.546 cm
d = 2r =2 × 2.546 cm = 5.09 cm
the relations between the angular and linear variables allows to find the result for the diameter of the cylinder is:
- The diameter is: d = 5.09 cm
Kinematics studies the movement of bodies, the movement being able to be linear, rotational or a combination of the two.
The linear and rotational movements are related, by the expressions.
x = θ r
v = w r
a = α r
Where x, v and a are the linear variables and θ, w and α the angular variables, r is the radius vector. For this relationship to be true, the angles must be measured in radians.
They indicate the angular speed of the cylinder is w = 7.5 rpm, reduce it to radians per second.
[tex]w = 7.5 \frac{rev}{min} (\frac{2\pi rad}{1 rev}) ( \frac{1 min}{60 s}) \\ w = 0.7854 \frac{rad}{s}[/tex]
we substitute in the relationship between the angular and linear variable.
v = w r
They indicate that the linear velocity is constant v = 2.0 cm/s = 2.0 10⁻²m/s.
[tex]r = \frac{v}{w}[/tex]
Let's calculate.
[tex]r = \frac{2 \ 10^{-2}}{0.7854}[/tex]
r = 2.546 10⁻² m = 2.546 cm
The diameter is twice the radius.
d = 2 r
d = 2 2.546 cm
d = 5.09 cm.
In conclusion using the relationships between the angular and linear variables we can find the result for the diameter of the cylinder is:
- The diameter is: d = 5.09 cm
Learn more about the relationship between angular and linear variables here: brainly.com/question/14312001
