What is the acceleration experienced by the tip of the 1.5 cm long sweep second hand on your wrist watch
1.6(10^-4)m/s^2
To calculate the acceleration experienced by the tip of the sweep second hand on a wristwatch, we first need to know the angular acceleration. The angular acceleration represents how quickly the hand is changing its rotation speed.
To calculate angular acceleration, we can use the formula:
Angular acceleration (α) = (Change in angular velocity) / (Change in time)
Next, we need to determine the linear velocity of the tip of the sweep second hand. The linear velocity is the speed at which the tip of the hand is moving in a straight line. It can be calculated using the formula:
Linear velocity (v) = (Radius of the hand) * (Angular velocity)
The radius of the watch hand is given as 1.5 cm. The angular velocity represents how fast the sweep second hand is rotating. In this case, the sweep second hand completes one revolution every 60 seconds (or 1 minute) since it takes a full minute to move from 12 to 12 on the watch dial.
First, let's calculate the angular acceleration. Since the angular velocity is constant (as the sweep second hand moves at a constant speed), the angular acceleration is 0.
Next, let's calculate the linear velocity using the formula mentioned above:
Linear velocity (v) = (Radius of the hand) * (Angular velocity)
The radius is given as 1.5 cm, and for one complete revolution, the angular displacement is 2π radians. Since it takes one minute to complete a full revolution, the time is 60 seconds.
Substituting the values into the formula:
v = (1.5 cm) * (2π radians) / (60 seconds)
Simplifying the equation:
v = (0.05π cm/s)
Therefore, the linear velocity is equal to approximately 0.157 cm/s.
Since the angular acceleration is 0, the acceleration experienced by the tip of the watch hand is also 0. This means that the hand is moving at a constant speed and not experiencing any change in its motion.