In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, tangential velocity, radial acceleration, tangential acceleration? Which of these quantities are zero throughout the motion?

In uniform circular motion, the following quantities are constant:

1. Speed: The speed of an object in uniform circular motion remains constant. Speed is defined as the magnitude of the instantaneous velocity.

2. Tangential velocity: Tangential velocity refers to the velocity along the tangent line to the circular path at any given point. In uniform circular motion, the magnitude of the tangential velocity remains constant. However, note that the direction of the tangential velocity changes continuously due to the circular path.

The following quantities are zero throughout the motion:

1. Radial acceleration: Radial acceleration represents the component of acceleration pointing towards the center of the circle. In uniform circular motion, the magnitude of the radial acceleration is zero, as the speed is constant and there is no change in the direction towards the center of the circle.

2. Tangential acceleration: Tangential acceleration refers to the component of acceleration directed tangentially to the circular path. In uniform circular motion, tangential acceleration is also zero, as there is no change in the speed or magnitude of the tangential velocity.

To summarize:

Constant throughout uniform circular motion:
- Speed
- Magnitude of tangential velocity

Zero throughout uniform circular motion:
- Magnitude of radial acceleration
- Magnitude of tangential acceleration

In uniform circular motion, several quantities remain constant, while some are zero throughout the motion. Let's analyze each of the quantities mentioned:

1. Speed: The speed is defined as the magnitude of the instantaneous velocity vector. In uniform circular motion, the speed remains constant. This is because the object moves at a consistent rate along the circular path.

2. Instantaneous Velocity: The instantaneous velocity is the vector that represents both the speed and direction of motion at a particular instant. In uniform circular motion, the instantaneous velocity is not constant as the direction is continuously changing. It is always tangent to the circular path, pointing in the direction of motion.

3. Tangential Velocity: The tangential velocity is the component of instantaneous velocity that is parallel to the tangent of the circular path. In uniform circular motion, the tangential velocity remains constant. It represents the velocity along the circular path.

4. Radial Acceleration: The radial acceleration is the component of acceleration that is directed towards the center of the circular path. In uniform circular motion, the radial acceleration is non-zero. Its value is given by the equation a = v^2 / r, where v is the magnitude of the tangential velocity and r is the radius of the circular path.

5. Tangential Acceleration: The tangential acceleration is the component of acceleration that is parallel to the tangent of the circular path. In uniform circular motion, the tangential acceleration is zero. This is because the speed remains constant, and there is no change in the magnitude of the tangential velocity.

To summarize:
- Constant quantities: speed, tangential velocity
- Non-zero but constant quantity: radial acceleration
- Zero quantity: tangential acceleration

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Tangential acceleration and speed are constant.

Tangential acceleration is zero