Calculate average velocity of a minute hand of 5cm long from between 6am to 6:30am
To calculate the average velocity of the minute hand of a clock from 6:00 am to 6:30 am, we need to determine the total angle covered by the minute hand in that time period.
The minute hand of a clock completes one full revolution, which is 360 degrees, in 60 minutes. Therefore, in 30 minutes (from 6:00 am to 6:30 am), the minute hand will cover half of that distance, which is 180 degrees.
The length of the minute hand is given as 5 cm. Since we have the angle covered by the minute hand, we can use this information to calculate the distance traveled by the tip of the minute hand.
The distance traveled by an object moving around a circle is equal to the circumference of the circle times the ratio of the angle covered to 360 degrees.
The formula to calculate the circumference of a circle is C = 2πr, where r is the radius of the circle. In this case, the radius is equal to the length of the minute hand, which is 5 cm.
So, the distance traveled by the tip of the minute hand in cm is:
Distance = (180/360) * 2π * 5
Next, we need to calculate the time taken for this distance to find the velocity. Since we know that the time period is 30 minutes, the time taken in hours is 30/60 = 0.5 hours.
Velocity is defined as the distance traveled divided by the time taken. Therefore, the average velocity of the minute hand in cm/hour is:
Average Velocity = Distance / Time
Substituting the values:
Average Velocity = [(180/360) * 2π * 5] / 0.5
Simplifying this expression will give us the final answer.
it travels PI radians.
Velocity=PI radians/30min*1min/60sec= PI/1800 rad/sec
that was angular velocity.
linear velocity= angular velocity*radius
linear velocity= .05 *PI/1800 m/s