A volmeter's pointer is 6 centimeters in length. Find an angle through which it rotates when it moves 2.5 centimeters on the scale.
The circumference is 2pi(6) or 12pi
let the angle be ߺ and set up a ratio
360/(12pi)= ß/2.5
ß = 2.5(360)/(12pi)
= 23.9º
or if α is the angle in radians
2pi/(12pi) = α/2.5
α = .417 radians
Thank You
To find the angle through which the voltmeter's pointer rotates, we can use the concept of similar triangles.
Let's assume that the voltmeter's pointer has rotated a certain angle θ, and it has moved 2.5 centimeters on the scale. The length of the pointer is 6 centimeters.
We can set up a proportion to calculate the angle θ:
(Length of movement on scale) / (Length of pointer) = (Angle of rotation) / 360°
Substituting the given values:
2.5 cm / 6 cm = θ / 360°
Now, we can solve for θ by cross-multiplying and dividing:
θ = (2.5 cm * 360°) / 6 cm
θ = 150°
Therefore, the angle through which the voltmeter's pointer rotates when it moves 2.5 centimeters on the scale is 150 degrees.
To find the angle through which the voltmeter's pointer rotates, we can use the concept of arc length and angle subtended.
The arc length is the distance traveled by the pointer on the scale, which in this case is given as 2.5 centimeters.
The formula to find the angle subtended by an arc on the circumference of a circle is:
θ = (s / r) * (180 / π)
Where:
θ is the angle subtended (in degrees).
s is the arc length.
r is the radius of the circle.
In this context, the voltmeter's pointer acts like an arc on the circumference of a circle. The radius of the circle is the length of the pointer, given as 6 centimeters.
Let's substitute the values into the formula:
θ = (2.5 / 6) * (180 / π)
To get the angle in degrees, we multiply the result by (180 / π):
θ ≈ (2.5 / 6) * (180 / π) ≈ 23.56 degrees
Therefore, the angle through which the voltmeter's pointer rotates when it moves 2.5 centimeters on the scale is approximately 23.56 degrees.