What is the angular speed of the tip of the minute hand on a clock in rad/s?

What is the angular speed of the tip of the minute hand on a clock,in rad/s?
How do I solve this?

Answer

General guidance

Concepts and reason

The concept used to solve this problem is angular kinematics. Initially, the full rotation in one hour for the minute hand can be calculated by considering the angular displacement of the minute hand. Then, time can be calculated for one full rotation. Finally, the angular speed of the minute hand can be calculated using the angular kinematics formula.

Fundamentals

The expression for the angular speed from kinematics equation is, Here, is the angular speed, is the angular displacement, and is the time for one full rotation.

Step-by-step

Step 1 of 2

For the minute hand on a clock, the full rotation in one hour is, Δθ = 2π rad The time taken for full rotation on a clock in one hour is, At=1 h
=1h(60 min
60 s)
1h
= 3600 s
1 min

The angular displacement for the minute hand is calculated for an hour and also the time taken for one full rotation is calculated by converting the time from hour to second.

Step 2 of 2

The expression for the angular speed is, Substitute 2n rad for and 3600 s for to find .

w
21 rad
=
3600 s
=1.74x10-rad/s

The angular speed of the minute hand is1.74x10-rads.


The angular speed of the minute hand is calculated using the angular kinematics equations. The angular speed depends on the angular displacement and time.

Answer

The angular speed of the minute hand is1.74x10-rads.


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