How Does a Ball's Velocity and Acceleration Change on a Circular Path?

In summary: Glad I could help. In summary, the conversation discusses a problem involving a ball moving in a circular path with a constant speed of 3.0 m/s and changing direction by 40.0 degrees in 1.75 seconds. The question asks for the change in velocity and acceleration during this time. The attempted solution involves finding the angular speed and translational speed, and using them to find the radius and acceleration. The final solution is found by accounting for the change in direction as the change in velocity.
  • #1
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18

Homework Statement


A ball moving in the circular path with a constant speed of 3.0 m/s changes direction by 40.0 degrees in 1.75 seconds. What is the change in velocity? What is the acceleration during the time?


Homework Equations


Fc = m * ac
ac = v^2/r


The Attempt at a Solution


No clue to be honest, the velocity shouldn't change, because of the acceleration. And we don't know the radius, so I'm not sure how to solve this at all
 
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  • #2
x86 said:
No clue to be honest, the velocity shouldn't change, because of the acceleration. And we don't know the radius, so I'm not sure how to solve this at all
Remember that velocity is a vector, with both a magnitude and a direction. If the direction changes, then there is acceleration.
 
  • #3
tms said:
Remember that velocity is a vector, with both a magnitude and a direction. If the direction changes, then there is acceleration.

Right, the only thing i can see is 40 degrees / 1.75 seconds.

Okay, so the acceleration has to be 3 m/s^2 every time it changes direction... So if the direction changes everyone 1 second for the velocity to be 3 m/s the acceleration would have to be 3 m/s^2. I'm getting closer, I think

WAIT! I think I did it.

Period.

T = (360 degrees) / ((40 degrees) / (1.75 s)) = 15.75 s

D = vt

2pir = v * 15.75 s

r = 3.0 m/s * 15.75 s / (2 pi) = 7.52007106 meters

ac = v^2 / r = 9.0 m^2/s^2 / 7.52 m =1.19680851 m / s^2 = 1.2 m/s^2

Now, to figure out velocity

1.2 m/s^2 * t = v

The final velocity = 1.2 m/s^2 * 1.75 s = 2 m/s

But it wants the change in velocity. I'm not sure what this means? What is change in velocity?
 
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  • #4
x86 said:
Right, the only thing i can see is 40 degrees / 1.75 seconds.
That is the angular speed. You also have the translational speed. Find a relation between those two quantities (that will give you [itex]r[/itex]).
Okay, so the acceleration has to be 3 m/s^2 every time it changes direction...
An object in uniform circular motion is always changing direction.
 
  • #5
tms said:
That is the angular speed. You also have the translational speed. Find a relation between those two quantities (that will give you [itex]r[/itex]).

An object in uniform circular motion is always changing direction.

Yes, I made an attempt at the solution and I think its right. But, what do they mean by change in velocity? I have no idea what this could mean.

The final velocity is 2.0 m/s. But the change would be something I'm not sure of. They could mean delta V, but then again that would give me an answer of 1.0 m/s, and the book says the answer is 2.0 m/s. But the book confirms the acceleration is correct.

EDIT: nevermind. i get it now.

The change in direction accounts for the change in velocity. Therefore, 1.2 m/s^2 * 1.75 seconds (time its changing) = 2.1 m/s which is the answer.

Thank you for those tips by the way, they helped me solve the problem. I totally forgot about period and such
 
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  • #6
x86 said:
But, what do they mean by change in velocity?
Change in velocity is just the definition of acceleration. It does sound a bit like a trick question, asking for the same thing twice using different words.
Thank you for those tips by the way, they helped me solve the problem. I totally forgot about period and such
You're welcome.
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. It can also be described as the spinning or turning of an object.

2. How is angular velocity different from linear velocity?

Angular velocity is a measure of the rate at which an object rotates or spins around an axis, while linear velocity is a measure of the rate at which an object moves in a straight line. Angular velocity is typically measured in radians per second, while linear velocity is measured in meters per second.

3. What is the difference between angular acceleration and linear acceleration?

Angular acceleration is the rate of change of angular velocity, while linear acceleration is the rate of change of linear velocity. In other words, angular acceleration measures how quickly an object's rotational speed is changing, while linear acceleration measures how quickly its linear speed is changing.

4. How do I calculate the moment of inertia for a rotating object?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. The formula for calculating moment of inertia is I = mr², where m is the mass of the object and r is the distance from the axis of rotation to the mass.

5. Can you explain the concept of torque in rotational motion?

Torque is a measure of the force that causes an object to rotate. It is calculated by multiplying the force applied to an object by the distance from the pivot point to the point where the force is applied. The SI unit for torque is Newton-meters (Nm).

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