What is the acceleration experienced by the tip of the 1.5 cm-long sweep second hand on your wrist watch?
To calculate the acceleration experienced by the tip of the sweep second hand on a wristwatch, we need to determine the speed and time it takes for the hand to complete a full revolution.
First, let's find the speed of the tip of the sweep second hand. The formula for speed is:
speed = distance / time
Since the sweep second hand completes a full revolution (360 degrees) every minute on a typical wristwatch, we will use the time taken for one minute, which is 60 seconds.
To find the distance covered by the tip of the sweep second hand, we can use the formula for the circumference of a circle:
circumference = 2 * π * radius
where π (pi) is approximately 3.14.
Given that the sweep second hand is 1.5 cm long, we can calculate the distance traveled by the tip during one revolution:
distance = circumference = 2 * π * radius = 2 * 3.14 * 1.5 cm
Now we have the distance covered by the tip and the time taken to complete it. Substitute these values into the speed formula:
speed = distance / time = (2 * 3.14 * 1.5 cm) / 60 s
The units will cancel out, and we will be left with cm/s as the unit of speed.
Finally, we need to find the acceleration. The formula for acceleration is:
acceleration = change in speed / time
Since we are assuming the hand is not changing its speed during the rotation, the change in speed is zero. Therefore, the acceleration of the tip of the sweep second hand on a wristwatch is zero.
To calculate the acceleration experienced by the tip of the sweep second hand on your wristwatch, we can use the formula for centripetal acceleration.
Centripetal acceleration is given by the equation:
a = v^2 / r
where v is the linear velocity and r is the radius of the circular path.
First, let's calculate the linear velocity of the tip of the sweep second hand.
The watch completes one full rotation in 60 seconds, which means the angular velocity (ω) is 2π radians per minute (or 2π/60 radians per second).
The linear velocity (v) can be calculated using the equation:
v = ω * r
where r is the length of the sweep second hand.
Given that the length of the sweep second hand is 1.5 cm (or 0.015 m), we can substitute values into the equation:
v = (2π/60) * 0.015
Now, let's calculate the linear velocity (v).
v = (2π/60) * 0.015
≈ 0.00157 m/s
Next, we can substitute the value of v into the centripetal acceleration formula:
a = v^2 / r
a = (0.00157)^2 / 0.015
≈ 0.0001647 m/s^2
Therefore, the acceleration experienced by the tip of the sweep second hand on your wristwatch is approximately 0.0001647 m/s^2.