The minute hand of a bedside clock is 2.5 cm long. In order for the clock to keep proper

time, the minute hand should maintain an average angular velocity of

IT makes one round (2PI radians) per hour,

speed= 2PIrad/hr*1hr/3600sec*2.5cm or
speed= 0.00436332313 cm/second

They ask for an angular velocity. That would be independent of the minute hand's length, and would be (2*pi rad/h)/(3600 sec/h) = 1.745*10^-3 rad/s

To determine the average angular velocity of the minute hand, we need to know the time it takes for the hand to complete one revolution, which is equivalent to 360 degrees.

The formula to calculate angular velocity is:

Angular velocity (ω) = θ / t

Where:
- ω is the angular velocity,
- θ is the angle covered in radians,
- t is the time taken to cover that angle in seconds.

Since we want to find the average angular velocity, we can assume that the time taken for one revolution is 60 minutes, or 3600 seconds (since there are 60 seconds in one minute).

Now, let's calculate the angle covered by the minute hand. The length of the minute hand can be used as the radius (r) of a circle:

Circumference (C) = 2πr

Substituting the length given (2.5 cm) as the radius, we get:

C = 2π(2.5) = 5π cm

To convert this into radians, we use the conversion factor that 2π radians is equal to 360 degrees:

1 radian = (360 degrees) / (2π)

So, the angle covered in radians (θ) is:

θ = (5π cm) * (1 radian / (360 degrees)) ≈ 0.0274 radians

Finally, we can calculate the average angular velocity by dividing the angle (θ) by the time taken (t):

ω = θ / t = 0.0274 radians / 3600 seconds ≈ 7.61 x 10^(-6) radians/second

Therefore, the minute hand should maintain an average angular velocity of approximately 7.61 x 10^(-6) radians/second to keep proper time.