the angular speed of the hour hand of a clock is
The minute takes one hour = 60 s/min × 60 min = 3600 s to go around, so ω = 2π / 3600 rad.s-1 = 1.7 × 10-3 rad.s-1. The hour hand takes 12 hours = 12 hours × 60 min/hour × 60 s/min = 43200 s to do 2π radians, so ω = 2π rad/43200 s = 1.5 × 10-4 rad.s-1. What is the angular velocity of the second hand?
6.28rad/rev * 2rev = 12.56 rad.
12.56rad/24h * 1h/3600s = 1.45*10^-4 rad/s.
The angular speed of the hour hand of a clock can be calculated using the formula:
Angular speed = 360 degrees / (12 hours * 60 minutes)
Here's the step-by-step calculation:
Step 1: Convert 12 hours to minutes:
12 hours * 60 minutes/hour = 720 minutes
Step 2: Divide 360 degrees by 720 minutes:
360 degrees / 720 minutes = 0.5 degrees/minute
Therefore, the angular speed of the hour hand of a clock is 0.5 degrees per minute.
To determine the angular speed of the hour hand of a clock, you need to know the time it takes for the hour hand to complete one full revolution (360 degrees).
Here are the steps to calculate the angular speed of the hour hand:
1. Determine the time it takes for the hour hand to make one full revolution. In a 12-hour clock, the hour hand completes one revolution in 12 hours.
2. Convert the time into seconds if necessary. Since we typically use seconds in angular speed calculations, convert 12 hours to seconds by multiplying it by 60 (minutes) and 60 (seconds).
12 hours × 60 minutes/hour × 60 seconds/minute = 43,200 seconds
3. Calculate the angular speed by dividing the angle (360 degrees) by the time it takes to complete one full revolution (in seconds):
Angular Speed = 360 degrees / 43,200 seconds
Simplifying the fraction, we get:
Angular Speed = 0.00833 degrees/second
Therefore, the angular speed of the hour hand of a clock is approximately 0.00833 degrees per second.