Acceleration at constant velocity?

[ma18]

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 acceleration 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?

 

[Chestermiller]

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 acceleration 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