Acceleration at constant velocity?

In summary: In other words, the particle must experience some force in order to maintain its speed and direction along the curved path. The equations for torque and acceleration are provided, and it is noted that constant speed implies that the derivative of speed with respect to time is zero, but this does not necessarily mean that the acceleration is zero. The direction of the velocity vector also plays a role in determining the acceleration. Therefore, maintaining constant speed on a cardiod requires both a constant speed and a constant direction.
  • #1
ma18
93
1

Homework Statement



Calculate the torque, t about origin that must be applied to a particle for it to maintain a constant speed v along a cardiod.

Homework Equations



t = r x f

a = (r_dot dot - r*Θ_dot ^2) r_hat + (r*Θ_dot dot + 2 r_dot * theta_dot) theta_hat

The Attempt at a Solution



Constant speed means that the derivative of the speed wrt time = 0 = magnitude of the acceleration. But then if the mag of the accleration is zero then everything turns to zero because it is all related. So I'm guess there is something else which constant speed implies and I am wrong. What is it?
 
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  • #2
ma18 said:

Homework Statement



Calculate the torque, t about origin that must be applied to a particle for it to maintain a constant speed v along a cardiod.

Homework Equations



t = r x f

a = (r_dot dot - r*Θ_dot ^2) r_hat + (r*Θ_dot dot + 2 r_dot * theta_dot) theta_hat

The Attempt at a Solution



Constant speed means that the derivative of the speed wrt time = 0 = magnitude of the acceleration. But then if the mag of the accleration is zero then everything turns to zero because it is all related. So I'm guess there is something else which constant speed implies and I am wrong. What is it?
Velocity is a vector quantity, so, if the direction of the velocity vector changes, that constitutes acceleration also. It's not only the speed that counts, it's also the direction.

Chet
 

Related to Acceleration at constant velocity?

1. What is acceleration at constant velocity?

Acceleration at constant velocity, also known as uniform acceleration, is the rate at which an object's velocity changes over time while traveling at a constant speed. This means that the object's direction or magnitude of velocity is changing at a constant rate.

2. How is acceleration at constant velocity calculated?

Acceleration at constant velocity is calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. Is acceleration at constant velocity the same as zero acceleration?

Yes, acceleration at constant velocity and zero acceleration are the same. This is because in both cases, the object's velocity is not changing over time.

4. What is the difference between acceleration at constant velocity and acceleration due to gravity?

The main difference between acceleration at constant velocity and acceleration due to gravity is the cause of the acceleration. Acceleration at constant velocity is caused by a change in direction or magnitude of velocity, while acceleration due to gravity is caused by the force of gravity pulling an object towards the Earth's surface.

5. Can an object have acceleration at constant velocity in a curved path?

Yes, an object can have acceleration at constant velocity in a curved path. This is because the object's velocity is changing in direction, even though its speed remains constant. This type of acceleration is known as centripetal acceleration.

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