Question

Express the angular velocity of a clock's second hand in the following units:

a) Degrees per minute
b) Radians per second
c) Revolutions per hour
d) Inches per second

Answer 1

The angular velocity of a clock's second hand is 360 degrees per minute, π/30 radians per second, 60 revolutions per hour, and for inches per second, it depends on the clock's radius, expressed as 2πr/60.

Step-by-step explanation:

To express the angular velocity of a clock's second hand in various units, we first need to establish the basic motion of the second hand.


In one minute, the second hand makes one complete revolution, which is 360 degrees, 2π radians, or 1 revolution.

• Degrees per minute: The second hand moves 360 degrees in one minute.
  
  
• Radians per second: To convert degrees per minute to radians per second, we use the conversion factor of π radians being equal to 180 degrees. This gives us (360°/60 s) × (π rad/180°) = 2π rad/60 s = π/30 rad/s.
  
  
• Revolutions per hour: Since there are 60 minutes in an hour and the second hand makes one revolution per minute, it makes 60 revolutions per hour.
  
  
• Inches per second: This value depends on the radius of the clock. For example, if the radius is 'r' inches, the second hand covers a distance of 2πr per minute. To convert to inches per second, divide by 60 (2πr/60).