Calculate the average angular velocity and the average linear velocity of the tip of a 10 cm long second hand of a watch..
To calculate the average angular velocity and average linear velocity of the tip of a second hand of a watch, we need to know the time it takes for the second hand to complete one revolution.
1. Start by finding the time it takes for the second hand to complete one revolution. In a standard analog clock, this is 60 seconds since the second hand completes one full rotation in 60 seconds.
2. Next, convert the length of the second hand from centimeters to meters. Since 1 meter is equal to 100 centimeters, the length of the second hand in meters is 0.10 meters (10 centimeters / 100).
3. To calculate the average angular velocity, use the formula:
Average Angular Velocity (ω) = 2π / Time taken for one revolution
In this case, the time taken for one revolution is 60 seconds (from step 1). Therefore,
Average Angular Velocity (ω) = 2π / 60
4. Calculate the average angular velocity:
Average Angular Velocity (ω) = 0.10472 rad/s (approximated to five decimal places)
5. To calculate the average linear velocity, use the formula:
Average Linear Velocity (v) = Distance traveled / Time taken for one revolution
In this case, the distance traveled is the circumference of a circle, which is calculated as:
Circumference = 2π * Radius
Since the radius is equal to the length of the second hand (0.10 meters), the circumference is:
Circumference = 2π * 0.10
Calculate the average linear velocity:
Average Linear Velocity (v) = (2π * 0.10) / 60
6. Calculate the average linear velocity:
Average Linear Velocity (v) = 0.01047 m/s (approximated to five decimal places)
So, the average angular velocity of the tip of the second hand is approximately 0.10472 rad/s, and the average linear velocity is approximately 0.01047 m/s.