Question

I am asked to find linear velocity and am given revolutions per minute. Since there are 2π radians in 1 revolution, I can convert rpm to radians per minute by multiplying by 2π. The angular displacement is 2π radians, so the angular velocity is 2π radians per minute. Next, I know that linear velocity is equal to angular velocity times the radius. Using 3.14 for π and multiplying 20π by 2 feet, I approximate the linear velocity as:

A) 125.6 feet per minute
B) 62.8 feet per minute
C) 251.2 feet per minute
D) 31.4 feet per minute

Answer 1

To calculate the linear velocity from revolutions per minute, convert rpm to radians per minute and then multiply by the radius. For 20 rpm with a radius of 2 feet, the linear velocity is 251.2 feet per minute.

Step-by-step explanation:

When given revolutions per minute (rpm) and asked to find linear velocity, you are on the right track by converting to radians per minute using the relationship that there are 2π radians in 1 revolution. Using an approximation for π as 3.14 and a radius of 2 feet, you'll need to first convert the given rpm to radians per minute and then use the formula for linear velocity (v = ωr), where v is the linear velocity, ω is the angular velocity, and r is the radius.

To solve for linear velocity using the given information (20 rpm and a radius of 2 feet):

• Convert rpm to radians per minute by multiplying by 2π, resulting in 20 * 2 * 3.14 rad/min = 125.6 rad/min.
• Multiply the angular velocity by the radius to get the linear velocity: 125.6 rad/min × 2 feet = 251.2 feet/min.

Therefore, the correct answer is C) 251.2 feet per minute, which represents the linear velocity of the rotating object.