A bolt is threaded onto one end of a thin horizontal rod,...

A bolt is threaded onto one end of a thin horizontal rod, and the rod is then rotated horizontally about its other end. An engineer monitors the motion by flashing a strobe lamp onto the rod and bolt, adjusting the strobe rate until the bolt appears to be in the same eight places during each full rotation of the rod (Fig. 6-75). The strobe rate is 2000 flashes per second; the bolt has mass $30 \mathrm{~g}$ and is at radius $3.5 \mathrm{~cm}$. What is the magnitude of the force on the bolt from the rod?

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Key Concepts

Rotational Motion

Rotational motion deals with the movement of objects along a circular path. In such scenarios, although an object might have constant speed, its velocity is continuously changing due to the change in direction, which requires a net force acting towards the center of the circle.

Centripetal Force

Centripetal force is the net inward force necessary to keep an object moving in a circular path. It is calculated using the relationship F = m?²r (or alternatively F = mv²/r), where m is the mass of the object, ? is its angular velocity, and r is the radius of the circular path.

Angular Velocity

Angular velocity is a measure of how fast an object rotates or revolves relative to another point, typically the center of the circle, and is commonly expressed in radians per second. It links the temporal aspects of circular motion to the dynamics, allowing for the calculation of centripetal acceleration and force.

Stroboscopic Effect

The stroboscopic effect occurs when a strobe light flashes at specific intervals, effectively 'freezing' the motion of a periodic system by only illuminating it at certain phases in its cycle. This technique helps in synchronizing and analyzing periodic motions, such as rotational motion, by making an object appear stationary or in discrete, repeating positions.

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