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What is the angle between velocity vecto...

What is the angle between velocity vector and acceleration vector in unitorm circular motion ?

A

`0^(@)`

B

`180^(@)`

C

`90^(@)`

D

`45^(@)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the angle between the velocity vector and the acceleration vector in uniform circular motion, we can follow these steps: ### Step 1: Understand Uniform Circular Motion In uniform circular motion, a particle moves along a circular path with a constant speed. Although the speed is constant, the direction of the velocity vector changes continuously. **Hint:** Remember that in uniform circular motion, the speed remains constant, but the direction of motion changes. ### Step 2: Identify the Velocity Vector The velocity vector (v) of the particle at any point on the circular path is tangent to the circle at that point. This means that the velocity vector is always directed along the tangent line to the circular path. **Hint:** Visualize the circular path and remember that the velocity vector is always tangent to the circle. ### Step 3: Identify the Acceleration Vector In uniform circular motion, the acceleration vector (a) is known as centripetal acceleration. This acceleration is directed towards the center of the circular path. It is responsible for changing the direction of the velocity vector, keeping the particle in circular motion. **Hint:** Recall that centripetal acceleration always points towards the center of the circle. ### Step 4: Determine the Angle Between the Vectors Since the velocity vector is tangent to the circle and the acceleration vector points towards the center, the angle between these two vectors is always 90 degrees (or π/2 radians). This is because the tangent line and the radius (which points towards the center) are perpendicular to each other. **Hint:** Use the geometric relationship between the tangent and radius to conclude that the angle is 90 degrees. ### Conclusion Thus, the angle between the velocity vector and the acceleration vector in uniform circular motion is 90 degrees. **Final Answer:** The angle between the velocity vector and the acceleration vector in uniform circular motion is 90 degrees. ---
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