Question

A body is moving in a circle of radius 1 unit (1cm, 1m, 1km). What is its linear velocity and angular velocity?

Answer 1

To determine the linear velocity and angular velocity of a body moving in a circle of radius 1 unit, we'll use the following formulas:

1. Linear velocity (v): The linear velocity is the speed at which an object moves along the circumference of the circle. It is given by the formula:

   v = r * ω

   Where:

   • v is the linear velocity
   • r is the radius of the circle
   • ω (omega) is the angular velocity

2. Angular velocity (ω): The angular velocity represents the rate at which the body rotates or moves around the center of the circle. It is given by the formula:

   ω = v / r

   Where:

   • ω (omega) is the angular velocity
   • v is the linear velocity
   • r is the radius of the circle

Let's calculate the linear velocity and angular velocity for different radii:

1. For a circle of radius 1 cm:

   • r = 1 cm = 0.01 m

   Linear velocity: v = r * ω = (0.01 m) * ω = 0.01ω m/s

   Angular velocity: ω = v / r = (0.01ω m/s) / (0.01 m) = ω rad/s

   Therefore, the linear velocity is 0.01ω m/s, and the angular velocity is ω rad/s.

2. For a circle of radius 1 m:

   • r = 1 m

   Linear velocity: v = r * ω = (1 m) * ω = ω m/s

   Angular velocity: ω = v / r = (ω m/s) / (1 m) = ω rad/s

   Therefore, the linear velocity is ω m/s, and the angular velocity is ω rad/s.

3. For a circle of radius 1 km:

   • r = 1 km = 1000 m

   Linear velocity: v = r * ω = (1000 m) * ω = 1000ω m/s

   Angular velocity: ω = v / r = (1000ω m/s) / (1000 m) = ω rad/s

   Therefore, the linear velocity is 1000ω m/s, and the angular velocity is ω rad/s.

In summary, the linear velocity depends on the angular velocity and the radius of the circle, while the angular velocity remains the same regardless of the radius, represented by ω rad/s.