the second hand of a watch is 15mm long. what is the linear velocity of the tip in m/s?
(2π * 15mm)/min * 1min/60s * 1m/1000mm = 0.00157 m/s
To calculate the linear velocity of the tip of the second hand of a watch, you need to know the length of the second hand and the angular velocity (rotation speed) of the hand.
Given:
Length of the second hand (r) = 15 mm = 0.015 m
The angular velocity (ω) of the second hand can be calculated using the formula:
ω = 2πf
Where:
f is the frequency of the second hand in Hz.
For a regular watch, the second hand completes one full rotation every 60 seconds or 1 revolution per minute.
Converting the frequency to Hz:
f = (1 revolution/minute) * (1 minute/60 seconds) = 1/60 Hz
Substituting the value of f into the formula gives:
ω = 2π(1/60) rad/s
Now we can calculate the linear velocity (v) using the formula:
v = r * ω
Substituting the values of r and ω:
v = (0.015 m) * (2π(1/60) rad/s)
Calculating the result:
v ≈ 0.00157 m/s
Therefore, the linear velocity of the tip of the second hand of the watch is approximately 0.00157 m/s.
To find the linear velocity of the tip of the second hand, you can use the formula:
V = ω * r
Where:
V is the linear velocity (in m/s),
ω is the angular velocity (in rad/s),
r is the length of the second hand (in meters).
First, we need to convert the length of the second hand from millimeters to meters. There are 1000 millimeters in a meter, so we can convert 15mm to meters by dividing it by 1000:
r = 15mm / 1000 = 0.015m
Now, we need to determine the angular velocity of the second hand. The second hand completes one full revolution (360 degrees) every 60 seconds. Since there are 2π radians in a full revolution, we can calculate the angular velocity as:
ω = (2π radians) / (60 seconds) = π/30 rad/s
Now, we have all the values we need to calculate the linear velocity:
V = ω * r = (π/30 rad/s) * (0.015m) = 0.00157 m/s
Therefore, the linear velocity of the tip of the second hand is approximately 0.00157 m/s.