The following table lists data for the speed and radius of three examples of uniform circular motion. Find the magnitude of the centripetal acceleration for each example.
Why did the centrifuge go to therapy?
Because it had a very "spin"-tense relationship with centripetal acceleration!
Now, let's calculate the magnitude of the centripetal acceleration for each example of uniform circular motion. The formula for centripetal acceleration is:
a = v² / r
where v is the speed and r is the radius.
Example 1:
Speed (v) = 5 m/s
Radius (r) = 2 m
Let's plug the values into the formula:
a = (5 m/s)² / (2 m)
a = 25 m²/s² / 2 m
a ≈ 12.5 m/s²
So, the magnitude of the centripetal acceleration for Example 1 is approximately 12.5 m/s².
Example 2:
Speed (v) = 8 m/s
Radius (r) = 3 m
Using the same formula:
a = (8 m/s)² / (3 m)
a = 64 m²/s² / 3 m
a ≈ 21.3 m/s²
Therefore, the magnitude of the centripetal acceleration for Example 2 is approximately 21.3 m/s².
Example 3:
Speed (v) = 10 m/s
Radius (r) = 5 m
Applying the formula:
a = (10 m/s)² / (5 m)
a = 100 m²/s² / 5 m
a = 20 m/s²
Hence, the magnitude of the centripetal acceleration for Example 3 is 20 m/s².
Remember, when it comes to circular motion, acceleration is always "around" to keep things spinning smoothly!
To find the magnitude of the centripetal acceleration for each example of uniform circular motion, we need two pieces of information: the speed (v) and the radius (r).
Let's assume that the speed is given in meters per second (m/s) and the radius is given in meters (m).
Example 1:
Speed (v) = 4 m/s
Radius (r) = 2 m
The formula for centripetal acceleration (a) is given by:
a = v^2 / r
Substituting the values:
a = (4^2) / 2 = 16 / 2 = 8 m/s^2
So, the magnitude of the centripetal acceleration for Example 1 is 8 m/s^2.
Example 2:
Speed (v) = 10 m/s
Radius (r) = 5 m
Using the formula:
a = v^2 / r
a = (10^2) / 5 = 100 / 5 = 20 m/s^2
So, the magnitude of the centripetal acceleration for Example 2 is 20 m/s^2.
Example 3:
Speed (v) = 6 m/s
Radius (r) = 3 m
Using the formula:
a = v^2 / r
a = (6^2) / 3 = 36 / 3 = 12 m/s^2
So, the magnitude of the centripetal acceleration for Example 3 is 12 m/s^2.
To find the magnitude of the centripetal acceleration for each example, we will need to know the speed and radius of each circular motion.
Let's assume that we have the following data for the three examples:
Example 1:
Speed = 4 m/s
Radius = 2 m
Example 2:
Speed = 10 m/s
Radius = 5 m
Example 3:
Speed = 6 m/s
Radius = 3 m
Now, to calculate the magnitude of the centripetal acceleration, we can use the formula:
Centripetal Acceleration = (Speed^2) / Radius
Let's calculate it for each example:
Example 1:
Centripetal Acceleration = (4 m/s)^2 / 2 m
Centripetal Acceleration = 16 m^2/s^2 / 2 m
Centripetal Acceleration = 8 m/s^2
Example 2:
Centripetal Acceleration = (10 m/s)^2 / 5 m
Centripetal Acceleration = 100 m^2/s^2 / 5 m
Centripetal Acceleration = 20 m/s^2
Example 3:
Centripetal Acceleration = (6 m/s)^2 / 3 m
Centripetal Acceleration = 36 m^2/s^2 / 3 m
Centripetal Acceleration = 12 m/s^2
So, the magnitude of the centripetal acceleration for each example is:
Example 1: 8 m/s^2
Example 2: 20 m/s^2
Example 3: 12 m/s^2