Physics

Physics

Problem

A bicycle wheel of radius 0.25 m0.25\,\text{m} starts from rest and its angular velocity increases uniformly at a rate of 4.0 rad s−24.0\,\text{rad}\,\text{s}^{-2}. Determine the magnitude of the tangential acceleration of a point on the rim.
Intuitive explanation

Tangential acceleration is the linear acceleration experienced by a point moving in a circle—it's what directly changes how fast that point is moving along its circular path. The key insight is that tangential acceleration is always proportional to angular acceleration through the radius: at=αra_t = \alpha r. Since the wheel's angular velocity increases uniformly, you have a constant angular acceleration, so you can directly convert it to the linear acceleration of the rim.

Intuitive explanation

Tangential acceleration is the linear acceleration experienced by a point moving in a circle—it's what directly changes how fast that point is moving along its circular path. The key insight is that tangential acceleration is always proportional to angular acceleration through the radius: at=αra_t = \alpha r. Since the wheel's angular velocity increases uniformly, you have a constant angular acceleration, so you can directly convert it to the linear acceleration of the rim.

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