a disk of a radius 50 cm rotates at a constant rate of 100 rpm. what distance in meters will a point on the outside rim travel during 30 seconds of rotation?
To find the distance traveled by a point on the outside rim of a rotating disk, we can use the formula:
Distance = Circumference × Number of rotations
First, let's find the circumference of the disk. The circumference of a circle can be calculated using the formula:
Circumference = 2 × π × Radius
In this case, the radius is given as 50 cm, so the circumference is:
Circumference = 2 × 3.14159 × 50 cm
Circumference ≈ 314.159 cm
Now, let's convert the distance from centimeters to meters:
Circumference in meters = Circumference in cm ÷ 100
Circumference in meters ≈ 314.159 cm ÷ 100
Circumference in meters ≈ 3.14159 meters
Next, we need to calculate the number of rotations in 30 seconds. Since the disk is rotating at a constant rate of 100 rpm (rotations per minute), we can calculate it as:
Number of rotations = Rotations per minute × Time (in minutes)
Number of rotations = 100 rpm × (30 seconds ÷ 60 seconds per minute)
Number of rotations = 100 rpm × 0.5
Number of rotations = 50 rotations
Now we can calculate the distance traveled by the point on the outside rim:
Distance = Circumference × Number of rotations
Distance = 3.14159 meters × 50 rotations
Distance ≈ 157.0795 meters
Therefore, a point on the outside rim of the disk will travel approximately 157.0795 meters during 30 seconds of rotation.