determine the linear velocity of a point rotating at 15 revolutions per minute at a distance of 3.04 meters from the center of a rotating object
one circumference = 2π(3.04) m or 6.08π m
so in 1 min the point covers 15(6.08π) or 91.2π m
linear velocity = 91.2π m/minute
Well, well, well, aren't we spinning around like a record baby, right round, round, round! Let's calculate that linear velocity, shall we?
First, we need to convert 15 revolutions per minute into radians per second. Since there are 2π radians in one revolution, we multiply 15 by 2π, and then divide by 60 to get the angular velocity in radians per second.
Next, to find the linear velocity, we multiply the angular velocity by the radius of the rotating point. In this case, our distance from the center is 3.04 meters.
So, my mathemagical friend, the linear velocity of that rotating point would be the angular velocity (in radians per second) multiplied by the radius (in meters). Armed with those tools, you can plow right through that problem!
To determine the linear velocity of a point rotating at 15 revolutions per minute at a distance of 3.04 meters from the center of a rotating object, you can use the formula:
Linear Velocity = 2πr × Angular Velocity
Where:
- Linear Velocity is the linear speed of the point.
- π (pi) is a mathematical constant approximately equal to 3.14159.
- r is the distance of the point from the center of rotation.
- Angular Velocity is the rate at which the object rotates, measured in radians per unit time.
First, we need to convert the given rotational speed from revolutions per minute to radians per second. Since 1 revolution is equal to 2π radians, we can calculate the angular velocity as follows:
Angular Velocity = (15 revolutions per minute) × (2π radians per revolution) / (60 seconds per minute)
Angular Velocity = (15 × 2π) / 60 radians per second
Next, we can substitute the values into the formula to calculate the linear velocity:
Linear Velocity = 2π × 3.04 meters × (15 × 2π) / 60 radians per second
Linear Velocity ≈ 2π × 3.04 × (15 × 2π) / 60 ≈ 6.09 meters per second
Therefore, the linear velocity of the point rotating at 15 revolutions per minute at a distance of 3.04 meters from the center of the rotating object is approximately 6.09 meters per second.
To determine the linear velocity of a point rotating at a given angular speed and distance from the center of rotation, you can use the formula:
Linear velocity = Angular speed * Radius
Step 1: Convert the given angular speed from revolutions per minute (rpm) to radians per second (rad/s). Since 1 revolution is equal to 2π radians, we have:
Angular speed (in rad/s) = (15 revolutions / 1 minute) * (2π radians / 1 revolution) * (1 minute / 60 seconds)
Angular speed = 15 * 2π / 60 ≈ 1.57 rad/s
Step 2: Plug the angular speed and the distance from the center into the formula:
Linear velocity = 1.57 rad/s * 3.04 meters
Linear velocity ≈ 4.77 meters per second
Therefore, the linear velocity of the point rotating at 15 revolutions per minute at a distance of 3.04 meters from the center of the rotating object is approximately 4.77 meters per second.