Calculate the Tangential Speed of a Lug Nut on a Rotating Wheel

What is the tangential speed of a lug nut on a wheel of a car if the lug nut is located 0.114 m from the axis of rotation and the wheel is rotating at 6.53 rev/sec?

The tangential speed of a lug nut on a wheel of a car can be calculated using the formula tangential speed = radius × angular speed. The radius is the distance from the axis of rotation to the lug nut, and the angular speed is the rotation rate of the wheel measured in radians per second. Let's calculate the tangential speed step by step.

Calculation of Tangential Speed:

Step 1: Convert the angular speed from revolutions per second to radians per second. Angular speed = 6.53 rev/sec × 2π rad/rev = 41.02 rad/sec.
Step 2: Calculate the tangential speed using the formula Tangential speed = Radius × Angular speed. In this case, the radius is 0.114 m, and the angular speed is 41.02 rad/sec.
Step 3: Plug in the values. Tangential speed = 0.114 m × 41.02 rad/sec = 4.68 m/s.
Therefore, the tangential speed of the lug nut on the rotating wheel is 4.68 m/s. The correct answer is option D.
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