Question

Consider a particle that moves in a plane with a constant radial velocity of v_r = 4 m/s starting from the origin. The angular velocity is constant and has magnitude omega = 2 rad/s.When the particle is 3m from the orgin:
A) Find the magnitude of the velocity

B) Find the magnitude of the acceleration

Answer 1

Answer:

The magnitude of the particle´s velocity is 4m/s (can´t change from the initial point to the final point) and the magnitude of the acceleration (centripetal acceleration) is 8 m/s². you have to considerate a particle moving with constant angular velocity (Uniform circular motion).

Explanation:

If the particle has constant angular velocity, you are in the presence of a uniform circular motion. That means the magnitude of the radial velocity is a constant and the relation between radial velocity and angular velocity is:

$\omega=R*v$         with R the circumference radius

In this kind of movement, the acceleration is perpendicular to the trajectory of the particle (centripetal acceleration). The expression of the magnitude of this acceleration is:

$A_{c} =\frac{v^{2} }{R} =v*\omega=4*2\frac{m}{s^{2}} =8\frac{m}{s^{2}}$