Linear Velocity: When to Use S/t or R*w

In summary, the formula v = S/t is used when given actual length and time, while v = R*w is used when given angular velocity or radius.
  • #1
Miike012
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Linear Velocity...

Homework Statement


When do I use
v = S/t
OR
v = R*w

s= arc length
w = angular velocity
t = time


Homework Equations





The Attempt at a Solution

 
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  • #2


You use the formulas that use the information you are given!

If you are given an "angular velocity" or an "radius", R, then you use v= Rw. If you are given an actual length and time, then you use v= S/T.
 
  • #3


the equation v = R*w shows that when you have a simple rotating object, and when w is constant (not changing), the linear velocity of the object (v) increases as you go further away from the origin (as R increases). As R increases, the object has to travel more but w is the same, so v must increase also.
 

FAQ: Linear Velocity: When to Use S/t or R*w

What is linear velocity?

Linear velocity is the rate of change of an object's position along a straight line. It is a measure of how fast an object is moving in a specific direction.

When is the formula S/t used for linear velocity?

The formula S/t, or distance divided by time, is used for calculating average linear velocity. It is used when the object's speed is constant over the entire period of time.

When is the formula R*w used for linear velocity?

The formula R*w, or radius multiplied by angular velocity, is used for calculating instantaneous linear velocity. It is used when the object's speed is changing over a short period of time, such as in circular or rotational motion.

What is the difference between linear velocity and angular velocity?

Linear velocity is the rate of change of an object's position along a straight line, while angular velocity is the rate of change of an object's angular position or rotation around a fixed point. Linear velocity is measured in units of distance per time, while angular velocity is measured in units of angle per time.

How are linear velocity and speed related?

Linear velocity and speed are closely related, but they are not the same. Speed is a scalar quantity that measures how fast an object is moving, while linear velocity is a vector quantity that measures both the speed and direction of an object's movement. This means that two objects can have the same speed, but different linear velocities if they are moving in different directions.

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