Calculate the average angular velocity and the average linear velocity of the tip of a 10 cm long second- hand of a watch.

omega = 2 pi radians/60 seconds = pi/30 rad/s

v = omega * r = (pi/30)(0.10) m/s

(assuming that the person's wrist is not moving and that the earth is stationary in space whatever that means :)

To calculate the average angular velocity and the average linear velocity of the tip of a 10 cm long second-hand of a watch, we need to know the time it takes for the second-hand to complete one revolution.

Let's assume the time it takes for the second-hand to complete one revolution is T seconds.

Step 1: Calculate the angular velocity:
The angular velocity (ω) is defined as the change in angle divided by the change in time.
Since the second-hand completes one revolution (360 degrees) in T seconds, the angular displacement (θ) is 360 degrees.
Therefore, the angular velocity (ω) can be calculated as:

ω = (360 degrees) / T

Step 2: Calculate the average linear velocity:
The linear velocity (v) can be calculated using the formula:

v = r × ω

Where r is the length of the second-hand, which is given as 10 cm.

Substituting the value of ω from Step 1 into the formula, we get:

v = (10 cm) × ω

Now we can substitute the value of ω from Step 1 and calculate the average linear velocity. However, please note that the units of ω need to match the units of T and r to get the correct units for v.

For example, if T is in seconds and r is in centimeters, then the units of ω should be degrees per second.

Once you have the value of T, you can calculate both the average angular velocity (ω) and the average linear velocity (v).

To calculate the average angular velocity, we need to know the time it takes for the second-hand to complete one revolution. Since we are given the length of the second-hand (10 cm), we can assume it traces out a circle of radius 10 cm.

The circumference of a circle is given by the formula: C = 2πr, where r is the radius of the circle. In this case, the circumference of the circle traced by the tip of the second-hand is 2π (10 cm) = 20π cm.

The time taken for the second-hand to complete one revolution is 60 seconds, as there are 60 seconds in a minute. Therefore, the average angular velocity can be calculated as:

Average Angular Velocity = (Total Angle Covered) / (Time Taken)
= (360°) / (60 seconds)
= 6°/ second

So, the average angular velocity of the tip of the second-hand is 6°/second.

To calculate the average linear velocity, we can use the formula:

Average Linear Velocity = (Average Angular Velocity) * (Radius)
= (6°/second) * (10 cm)
= 60 cm/second

Hence, the average linear velocity of the tip of the 10 cm long second-hand is 60 cm/second.