Question

Angular velocity of the hour hand of a clock

Answer 1

Answer:

Explanation:

The angular velocity is independent of the clock size, however for larger clocks the linear velocity of the pointers at the end of the hands will be greater.

The second hand goes through 2π radians in 1 min, or 2π radian/60 seconds,

so ω = π/30 rad.s-1 = 0.03 rad.s-1.

The minute takes one hour = 60 s/min × 60 min = 3600 s to go around,

so ω = 2π / 3600 rad.s-1 = 1.7 × 10-3 rad.s-1.

The hour hand takes 12 hours = 12 hours × 60 min/hour × 60 s/min = 43200 s to do 2π radians,

so ω = 2π rad/43200 s = 1.5 × 10-4 rad.s-1.

Answer 2

Answer:

Explanation:

The hour hand of the clock does not actually have a uniform instantaneous angular velocity but we can find its average angular velocity.

In a time period of 12 hours the hour hand moves an entire revolution.

ω=ΔθΔtω=ΔθΔt

ω=2π rad12⋅60⋅60 sω=2π rad12⋅60⋅60 s

ω=π21600 rad s−1ω=π21600 rad s−1