The second hand of a watch is 1.5cm long. Find the linear speed of a point on the second hand at a distance of 0.5 cm from the tip. Express your answer in 3 signficant digits.

Sure, here's how you can solve this problem:

Step 1: Understand the problem The second hand of a watch completes a full circle (360 degrees) in 60 seconds. The point on the second hand that is 0.5 cm from the tip is actually 1 cm from the center of the watch (since the total length of the second hand is 1.5 cm).

Step 2: Calculate the circumference of the circle The point on the second hand moves in a circular path with a radius of 1 cm. The circumference of this circle is given by the formula 2πr, where r is the radius. Substituting r = 1 cm, we get the circumference as 2π cm.

Step 3: Calculate the linear speed The linear speed is defined as the distance traveled per unit time. In this case, the point on the second hand travels a distance of 2π cm in 60 seconds. Therefore, the linear speed is 2π/60 cm/s.

Step 4: Round to 3 significant digits The value of π is approximately 3.14159. Therefore, the linear speed is approximately 0.10472 cm/s. Rounding this to 3 significant digits, we get the linear speed as 0.105 cm/s.