Question

Express the angular velocity of the second hand on a clock in the following units :

Part A : rev/hr
Part B : deg/min
Part C : red/s

Answer 1

The angular velocity of the second hand on a clock is 60 rev/hr, 360 deg/min, and π/30 rad/s. The angular velocity vector, according to the right-hand rule, points into the wall.

Step-by-step explanation:

To express the angular velocity of the second hand on a clock, we need to consider that the second hand completes one revolution every 60 seconds or one minute. Therefore, we can calculate the angular velocity in various units as follows:

Part A: revolutions per hour (rev/hr) - Since the second hand completes one revolution per minute, there are 60 revolutions in one hour. Hence, the angular velocity in rev/hr is 60 rev/hr.

Part B: degrees per minute (deg/min) - One revolution is equivalent to 360 degrees. Because the second hand completes one revolution per minute, the angular velocity in deg/min is 360 deg/min.

Part C: radians per second (rad/s) - To convert degrees per minute to radians per second, we use the conversion factor that 360 degrees is equal to 2π radians. Since there are 60 seconds in one minute, we convert 360 deg/min to radians per second by dividing by 60 and multiplying by π/180. This gives us an angular velocity in rad/s of 2π rad/60 s or π/30 rad/s.

Regarding the direction of the angular velocity vector of the second hand, by the right-hand rule, since the second hand rotates clockwise, the angular velocity vector is directed into the wall.