I'm afraid that I don't understand the question.pcsx22 said:Homework Statement
the magnitude of tangential velocity is same but the directions are different..so how can the tangential acceleration be zero??Homework Equations
The Attempt at a Solution
pcsx22 said:Homework Statement
the magnitude of tangential velocity is same but the directions are different..so how can the tangential acceleration be zero??
Homework Equations
The Attempt at a Solution
Pi-Bond said:You just answered the question yourself; it's because the tangential velocity (magnitude) is the same. If there were any tangential acceleration, the magnitude would not be constant. The only acceleration in this case is normal acceleration (i.e. centripetal acceleration) which causes the direction to change.
The velocity vector continually changes direction. Any change in velocity, magnitude or direction, is an acceleration. In uniform circular motion, the magnitude (speed) doesn't change but the direction does. The tangential component of acceleration is zero, but the radial component is not.pcsx22 said:if tangential acceleration is considered to be zero in uniform circular motion then why is uniform circular motion is called accelerated motion??
Tangential acceleration is the rate of change of tangential velocity with respect to time. In uniform circular motion, the speed of the object remains constant, but the direction of the velocity changes continuously. This change in direction causes a tangential acceleration that is always perpendicular to the velocity vector.
In uniform circular motion, the object moves at a constant speed and follows a circular path. Since the speed is constant, there is no change in the magnitude of the tangential velocity. Therefore, the tangential acceleration is zero.
In uniform circular motion, the object experiences a centripetal acceleration, which is always directed towards the center of the circle. This acceleration is necessary to keep the object moving in a circular path. Since the centripetal acceleration is always perpendicular to the tangential velocity, it does not affect the magnitude of the tangential velocity. Therefore, the tangential acceleration remains zero.
The tangential acceleration is inversely proportional to the radius of the circle. This means that as the radius of the circle decreases, the tangential acceleration increases, and vice versa. This relationship is described by the formula a_t = v^2/r, where v is the tangential velocity and r is the radius of the circle.
In non-uniform circular motion, the speed of the object changes, and therefore, the tangential acceleration is not zero. In this case, the tangential acceleration is responsible for changing the speed of the object, while the centripetal acceleration is still responsible for changing the direction of the velocity. The combination of these two accelerations results in a curved path rather than a perfect circle.