The Speedy Track Star: Calculating Angular Velocity
What is the angular velocity of the track star running a 430 m race on a 430 m circular track in 50 seconds?
Final answer: To calculate the angular velocity, we use the formula ω = Δθ/Δt. For a full circle or revolution (as in this case), Δθ is 2π radian and Δt is the time taken, 50 seconds. Hence the angular velocity is 2π/50 or 0.126 rad/s.
Calculating Angular Velocity of the Track Star
To calculate the angular velocity of the track star, we use the formula ω = Δθ/Δt. In this case, the track star completes a full circle on the 430 m circular track, which corresponds to a change in angular position of 2π radians. The time taken for this complete revolution is 50 seconds. By substituting the values into the formula, we find that the angular velocity is 0.126 rad/s.
Exploring Angular Velocity in the Track Star's Race
Angular velocity is a measure of how quickly an object rotates around a specific point or axis. In the context of the track star's race, the angular velocity indicates how fast he completes a full lap around the circular track.
The formula for calculating angular velocity is ω = Δθ/Δt, where ω represents angular velocity, Δθ is the change in angular position, and Δt is the change in time. In this scenario, the track star's angular velocity is determined by the time taken to complete a full revolution and the corresponding change in angular position.
By substituting the values from the given data into the formula, we obtain the angular velocity of the track star to be 0.126 rad/s. This value signifies the speed at which the track star rotates around the circular track, showcasing his agility and efficiency in completing the race.