Question

What steps did you incorporate into your response for calculating angular and linear velocity? Check all that apply.

a) Multiplying revolutions per minute by 2π to obtain angular velocity in radians per minute.
b) Approximating linear velocity by multiplying angular velocity by the radius.
c) Verifying the calculation by dividing linear velocity by the radius to determine angular velocity.
d) Assessing the reasonableness of the answer by finding the arc length for 10 revolutions.

Answer 1

To calculate angular and linear velocity, one would multiply revolutions per minute by 2π to find angular velocity in radians, approximate linear velocity by multiplying angular velocity by radius, verify calculations, and assess reasonableness using arc length for checks.

Step-by-step explanation:

When calculating angular and linear velocity, the steps incorporated into the response involve:

1. Multiplying revolutions per minute by 2π to obtain angular velocity in radians per minute.
2. Approximating linear velocity by multiplying angular velocity by the radius.
3. Verifying the calculation by dividing linear velocity by the radius to determine angular velocity.
4. Assessing the reasonableness of the answer by finding the arc length for 10 revolutions.

Regarding a particle that moves 3.0 m along a circle of radius 1.5 m, the angle through which it rotates can be found by taking the traveled arc length and dividing it by the circle's radius, which gives an angular rotation in radians. If the particle makes this trip in 1.0 second, the angular velocity can be found by dividing the angle by the time. Additionally, the linear velocity is found by multiplying the radius by the angular velocity, giving the velocity in meters per second (m/s).