Calculate the speed at the edge of a disc of radius 8.5 cm that rotates at the rate of 4 rev/s. Answer should be in units of m/s
Thanks
change the rev to radians by multiplying by 2PI
speededge=angularspeed*radius
= 2PI*.085*4 m/s
Why did the disc go on a diet?
Because it wanted to be lighter and faster!
Now, let's calculate the speed at the edge of the disc.
The circumference of the disc can be calculated using the formula:
C = 2πr
where r is the radius of the disc.
Given that the radius is 8.5 cm, we need to convert it to meters:
r = 8.5 cm = 0.085 m
Substituting the value of the radius into the formula, we get:
C = 2π(0.085) = 0.17π m
Since the disc rotates at a rate of 4 revolutions per second, the speed can be calculated by multiplying the circumference by the rate of revolution:
Speed = 0.17π * 4 m/s
Calculating this, we get:
Speed ≈ 2.136 m/s
So, the speed at the edge of the disc is approximately 2.136 m/s. Keep spinning, little disc!
To calculate the speed at the edge of a disc, we need to find the circumference of the disc first. The circumference (C) of a disc is given by the formula:
C = 2πr
where r is the radius of the disc.
In this case, the radius of the disc is given as 8.5 cm. We need to convert it to meters:
r = 8.5 cm = 8.5/100 m = 0.085 m
Next, we need to find the angular speed (ω) of the disc. The angular speed is given by the formula:
ω = 2πf
where f is the frequency of rotation in Hz.
In this case, the frequency of rotation is given as 4 rev/s. We need to convert it to Hz:
f = 4 rev/s = 4 Hz
Now, we can calculate the angular speed as follows:
ω = 2πf = 2π * 4 = 8π rad/s
Finally, we can calculate the speed at the edge of the disc by multiplying the angular speed by the radius:
v = ωr = (8π rad/s) * (0.085 m) ≈ 0.678 m/s
Therefore, the speed at the edge of the disc is approximately 0.678 m/s.
To calculate the speed at the edge of a rotating disc, you can use the formula:
Speed (v) = 2 * π * radius * frequency
In this case, the radius of the disc is given as 8.5 cm, which is equal to 0.085 m (since 1 m = 100 cm). The frequency (f) is given as 4 rev/s.
Substituting these values into the formula, we get:
v = 2 * π * 0.085 m * 4 rev/s
Simplifying the expression, we have:
v = 2 * π * 0.085 m * 4 rev/s
v = 0.68 * π m/s
Calculating this value, we get:
v ≈ 2.14 m/s (rounded to two decimal places)
So, the speed at the edge of the disc is approximately 2.14 m/s.