Can Circular Motion Be Calculated Like Linear Motion?

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In summary, When learning about circular motion, a common question is whether the arc length of a ball's motion can be calculated the same way as linear motion. By applying a force perpendicular to the ball's motion, the distance traveled can be calculated using the formula d={v_i}t+\frac{F{t^2}}{2m}. Additionally, the angular velocity can be found by dividing the force by the product of the mass and radius. However, if the force is always in the direction of the circular motion, the angular velocity is not the total distance divided by the radius, but rather the angle.
  • #1
clm222
Hi, quick question
I've just started to learn circular motion and i tried a basic force problem.

Imagine there is a ball on a string with a string length 'r', and a ball mass 'm'.
You apply a force 'F' for one second. Can the arc length of the ball's motion be calculated the same as linear motion? [itex]d=\frac{F{t^2}}{2m}[/itex] (replacing acceleration with F/m, vi=0)
Can I also go as far as the find the angular velocity by dividing by the radius?
[tex]ω=\frac{F{t^2}}{2mr}[/tex]

Thanks.
 
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  • #2
Where, and in which direction, do you apply the force?
If the force is always in direction of the circular motion (as forced by the string), that works. However, angular velocity after the acceleration is not the total distance divided by the radius. That is the angle, not its velocity.
 
  • #3
oh ok,
so if i were to have the force constantly be applied perpendicular to the ball than i CAN use the distance formula?

if so, let's say the ball has initial velocity 'vi', and a force is applied, the final velocity can be calculated using [itex]{v_f}={v_i}+\frac{Ft}{m}[/itex], could i also calculate the distance travled: [itex]d={v_i}t+\frac{F{t^2}}{2m}[/itex] ?
 
  • #4
If the force is applied perpendicular to the motion of the ball then its speed is constant. The distance around the circle in time t is [itex]v_it[/itex].
 
  • #5


Hello, great question! In circular motion, the arc length of the ball's motion cannot be calculated in the same way as linear motion. This is because the ball is moving in a curved path, rather than a straight line. To calculate the arc length, you would need to use the formula s=rθ, where r is the radius and θ is the angle of rotation.

As for finding the angular velocity, you are correct in saying that it can be calculated by dividing the linear velocity by the radius. However, in this case, your formula for linear velocity (d=Ft^2/2m) is incorrect. It should be v=at, where a is the acceleration caused by the force F. Then, using the relationship between linear and angular velocity (v=rω), you can find the angular velocity.

I hope this helps clarify your understanding of circular motion. Keep up the good work in your studies!
 

1. What is the difference between velocity with an axis and without an axis?

Velocity is a physical quantity that describes the rate of change of an object's position over time. When an axis is included, it provides a reference point or direction for the velocity. Without an axis, the velocity is simply the magnitude of the object's speed.

2. How do you calculate velocity with an axis?

To calculate velocity with an axis, you need to know the object's displacement in a certain direction and the time it takes to travel that distance. The formula for velocity with an axis is velocity = displacement / time.

3. Can velocity with an axis be negative?

Yes, velocity with an axis can be negative. This indicates that the object is moving in the opposite direction of the chosen axis. For example, if the axis is pointing to the right and the velocity is -10 m/s, the object is moving to the left at a speed of 10 m/s.

4. Why is velocity with an axis important in physics?

Velocity with an axis is important in physics because it allows us to describe the direction and magnitude of an object's motion. This is crucial in understanding and predicting the behavior of objects in the physical world.

5. What is the difference between velocity and speed?

Velocity and speed are closely related but have distinct differences. Velocity includes both the magnitude and direction of an object's motion, while speed only refers to the magnitude. In other words, velocity takes into account the direction of an object's motion, while speed does not.

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