To find the acceleration and velocity of a body moving in a circular orbit, we can use the following formulas:
Velocity (v) = radius (r) × angular speed (ω) Acceleration (a) = radius (r) × angular speed squared (ω²)
Given: Mass of the body (m) = 10 kg Radius of the orbit (r) = 0.5 m Angular speed (ω) = 5 rad/s
Let's calculate the velocity first:
Velocity (v) = r × ω = 0.5 m × 5 rad/s = 2.5 m/s
The velocity of the body moving in the circular orbit is 2.5 m/s.
Now, let's calculate the acceleration:
Acceleration (a) = r × ω² = 0.5 m × (5 rad/s)² = 0.5 m × 25 rad²/s² = 12.5 m/s²
The acceleration of the body moving in the circular orbit is 12.5 m/s².