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The 4.5 cm long second hand on a watch rotates smoothly. What is its angular velocity? What is the speed of the tip of the hand?

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Angular velocity means how many radians/degrees is this hand passing by every second.
First, you realize it goes through a whole revolution (2[tex] \pi [/tex] in radians) in 60 seconds.
This means for every second, it passes by:
[tex] \frac{2 \pi }{60 s} = 0.105 \frac{rad}{sec} [/tex]

For the next part, you need to know this equation:
Tangential velocity=Angular velocity x radius (meters)
[tex]velocity=0.105 \frac{rad}{sec} *0.045m[/tex]
[tex]velocity=0.004725 \frac{meters}{sec} [/tex]
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