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Question

Calculate the angular speed of the second hand, minute hand and hour hand of clock?

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Solution

Step 1: Formula used:
Angular speed(ω) = Angulardisplacement(θ)Totaltimetaken(t)
Step 2: Calculation of the angular speed of second hand of the clock:
The second hand of the clock completes one round in 60sec.
The angular displacement that is; the angle covered by the second hand of the clock in one complete round is 2π radian.
That is; θ=2πradian
t=60sec
Thus,
The angular speed of second hand of the clock is;

ωs=2πradian60sec

ωs=π30rads1

ωs0.105rads1

Step 3: Calculation of angular speed of minute hand of the clock:

The second hand of the clock completes one round in 60minutes.

60minutes=60×60sec

=3600sec

The angular displacement that is; the angle covered by the minute hand of the clock in one complete round is 2π radian.

Thus,

The angular speed of the minute hand;

ωm=2πradian3600sec

ωm=π1800rads1

ωm1.745×103rads1

Step 4: calculation of angular speed of hour hand of the clock:

The second hand of the clock completes one round in 12 hours.

12hours=12×60×60sec

=720×60sec

=43200sec

The angular displacement that is; the angle covered by the hour hand of the clock in one complete round is 2π radian.

Then,

The angular speed of the hour hand of the clock will be;

ωh=2πradian43200sec

ωh=π21600rads1

ωh1.45×104rads1

Thus,

The angular speed of second hand of the clock = π30rads1 0.105rads1 =

The angular speed of minute hand of the clock = π1800rads1 1.745×103rads1

The angular speed of minute hand of the clock = π21600rads1 1.45×104rads1


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