What is the angular speed in radians per second of the hour hand of a clock? If the hand is 5cm long, how fast is the tip moving in millimeters per second?

Express the following angular speed in radians per second. Find 10 revolution in seconds and choose the correct answer:

To calculate the angular speed of the hour hand of a clock, we need to know the time it takes for the hour hand to make one complete revolution around the clock's face.

In most clocks, the hour hand completes one full rotation in 12 hours (or 720 minutes). Therefore, the angular speed is given by:

Angular Speed = (2π radians) / (720 minutes)

Simplifying this equation, we get:

Angular Speed = π / 360 radians per minute

To convert the angular speed from minutes to seconds, we divide by 60:

Angular Speed = (π / 360) radians / (60 seconds)

Now let's calculate the angular speed:

Angular Speed ≈ 0.000145 rad/s

To calculate the linear speed of the tip of the hour hand, we can multiply the angular speed by the length of the hand. In this case, the length of the hour hand is given as 5 cm:

Linear Speed = Angular Speed * Length of the hand

Let's calculate the linear speed:

Linear Speed = 0.000145 rad/s * 5 cm

Since the answer needs to be in millimeters per second rather than centimeters per second, we can convert centimeters to millimeters by multiplying by 10:

Linear Speed ≈ 0.000725 mm/s

Therefore, the tip of the hour hand moves at a speed of approximately 0.000725 millimeters per second.