A car is up on a hydraulic at a garage. The wheels are free to rotate, and the drive wheels are rotating with a constant angular velocity. Does a point on the rim of the wheel have (A) a tangential velocity, (B) a tangential acceleration and (C) a centripetal acceleration?
Yes, No, Yes
(A) Yes, a point on the rim of the wheel has a tangential velocity. The tangential velocity is the linear velocity (speed) of the point as it moves along the circumference of the wheel.
(B) No, a point on the rim of the wheel does not have a tangential acceleration. Tangential acceleration refers to changes in the linear velocity of an object. Since the drive wheels are rotating with a constant angular velocity, there is no change in the linear velocity, and hence no tangential acceleration.
(C) Yes, a point on the rim of the wheel has a centripetal acceleration. Centripetal acceleration is the acceleration directed towards the center of the circular path. In this case, as the wheel rotates, the point on the rim is continuously changing its direction towards the center of the wheel, resulting in a centripetal acceleration.
To determine whether a point on the rim of the wheel has tangential velocity, tangential acceleration, and centripetal acceleration, let's break down each concept:
(A) Tangential Velocity:
Tangential velocity refers to the speed of an object traveling along a curved path. A point on the rim of a rotating wheel does have tangential velocity. This is because as the wheel spins, each point on its rim moves in a circular motion, and the speed at which it moves tangentially depends on the angular velocity (rate of rotation) of the wheel.
(B) Tangential Acceleration:
Tangential acceleration measures how the tangential velocity of an object changes over time. In this scenario, since the drive wheels are rotating with a constant angular velocity, the tangential acceleration would be zero. This is because there is no change in the speed of the wheel, and therefore no change in its tangential velocity.
(C) Centripetal Acceleration:
Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. A point on the rim of the wheel does experience centripetal acceleration. This acceleration is essential to keep the object moving in a circular path and is directed towards the center of the wheel.
To summarize:
(A) The point on the rim of the wheel has tangential velocity.
(B) The point on the rim of the wheel has zero tangential acceleration.
(C) The point on the rim of the wheel experiences centripetal acceleration directed towards the center of the wheel.