Also Check – Heat Input Formula
V = rω
Here, V represents tangential velocity, r is the radius of the circular path, and ω (omega) stands for angular velocity. The angular velocity measures the rate of change of the angle as an object moves in a circular path.Also Check – Heat Of Vaporization Formula
Also Check – Strain Formula
Example 3 : Calculating Tangential Velocity of a Car Wheel Suppose a car's wheel has a radius of 0.4 meters and an angular velocity of 6 radians per second. Calculate the tangential velocity of the car's wheel Solution: To find the tangential velocity (Vt), we can use the formula: V = rω Where: - r (radius) = 0.4 meters - ω (angular velocity) = 6 radians per second Now, let's calculate Vt: V = (0.4 meters) x (6 radians/second) = 2.4 meters/second The tangential velocity of the car's wheel is 2.4 meters per second. Example 4 : Tangential Velocity of a Rotating Fan Blade A ceiling fan blade has a radius of 0.5 meters and an angular velocity of 4 radians per second. Find the tangential velocity of the ceiling fan blade. Solution: Using the formula Vt = rω: V= (0.5 meters) x (4 radians/second) = 2 meters/second The tangential velocity of the ceiling fan blade is 2 meters per second. Example 5 : Circular Motion in a Carousel In an amusement park, a carousel has a radius of 8 meters and completes one rotation in 10 seconds. Calculate the tangential velocity of a horse on the outer edge of the carousel.Solution:
First, we need to find the angular velocity (ω). Since the carousel completes one rotation in 10 seconds, the angular velocity is: ω = 2π / time = 2π / 10 seconds = 0.2π radians/second Now, calculate the tangential velocity using the formula: V = rω V= (8 meters) x (0.2π radians/second) ≈ 5.03 meters/second The tangential velocity of the horse on the outer edge of the carousel is approximately 5.03 meters per second. Example 6 : Rotating Ferris Wheel A Ferris wheel has a radius of 20 meters and completes one rotation in 30 seconds. Calculate the tangential velocity of a passenger cabin on the Ferris wheel.Solution:
First, find the angular velocity (ω): ω = 2π / time = 2π / 30 seconds ≈ 0.2094 radians/second Now, calculate the tangential velocity using the formula: V = rω V = (20 meters) x (0.2094 radians/second) ≈ 4.188 meters/second The tangential velocity of the passenger cabin on the Ferris wheel is approximately 4.188 meters per second. Example 7 : Tangential Velocity in a Wind Turbine A wind turbine blade has a radius of 15 meters and an angular velocity of 2 radians per second. Determine the tangential velocity of the wind turbine blade.Solution:
Using the formula Vt = rω: V = (15 meters) x (2 radians/second) = 30 meters/second The tangential velocity of the wind turbine blade is 30 meters per second. These solved questions illustrate how to calculate tangential velocity in various scenarios, which is essential in understanding rotational motion in different contexts. Formulas In addition to the primary formula for tangential velocity, it's worth noting some related equations that play a crucial role in rotational motion: Centripetal Acceleration (ac): This represents the acceleration of an object moving in a circular path and is given by the formula ac = rω², where r is the radius and ω is angular velocity. Linear Speed (V): This is the speed of an object moving along a circular path and is related to tangential velocity by the equation Vl = rω. In conclusion, tangential velocity is a concept that bridges the gap between the theoretical and practical aspects of rotational motion. From its historical roots to its applications in diverse fields like astronomy, engineering, and sports, tangential velocity is an indispensable component of our understanding of the physical world. It enables us to analyze, design, and optimize systems that involve circular motion. We've explored the fundamental formula for tangential velocity and provided solved examples to enhance comprehension. With this knowledge, you can better appreciate the role of tangential velocity in our daily lives and in scientific exploration.