# Compute the speed of the tip of the second hand

• smoki
In summary, the conversation discusses how to compute the speed and velocity of a watch's second hand, as well as its change in velocity and average vector acceleration between certain time intervals. It also mentions the use of unit vectors to indicate direction.
smoki
I think this is a simple question but I'm not sure if I'm doing it right, this is what I have so far...

A watch has a second hand 2.0 cm long.

a) Compute the speed of the tip of the second hand.

C = 2pi(r) r = 2.0cm = 0.02m - leave as cm or convert to m?

V = [2pi(0.02m)]/60s = 2.1 x 10^-3 m/s - divide by 60s?

b) What is the velocity of the tip of the second hand at 0.0s ? At 15 seconds?

well 0s=60s right...? if so then the answer is the same as a)

for 15s V=[2pi(0.02m)]/15s = 8.3 x 10^-3 m/s

c) Compute its change in velocity between 0.0 and 15 seconds.

?

d) Compute its average vector acceleration between 0.0 and 15 seconds.

I think I could answer this if I could figure out c)

Part A looks correct.

For part B, remeber that velocity is a vector...amplitude and direction. Therefore the velocity at 0/60 sec is (using the i designator as a unit vector in the +x direction) $$\vec{v} = 2.1 x 10^{-3} \hat{i}$$. At 15 seconds, the direction is going to be down (using j as the unit vector in the +y direction), in the -j direction with the same magnitude.

Does that point out what you need to do for the rest of the problems?

a) To compute the speed of the tip of the second hand, we can use the formula v = 2πr/t, where r is the radius (length) of the second hand and t is the time in seconds. In this case, r = 2.0 cm = 0.02 m and t = 60 seconds (as the second hand completes one full rotation in 60 seconds). So the speed of the tip of the second hand is: v = (2π*0.02m)/60s = 0.0021 m/s.

b) The velocity of the tip of the second hand at 0 seconds is the same as the answer in part a), which is 0.0021 m/s. At 15 seconds, the second hand has completed 1/4th of a rotation, so we can use the formula v = (2π*0.02m)/(1/4*60s) = 0.0083 m/s.

c) The change in velocity between 0 and 15 seconds can be calculated by taking the difference between the velocities at these two times. So the change in velocity is: 0.0083 m/s - 0.0021 m/s = 0.0062 m/s.

d) To compute the average vector acceleration, we need to know the initial and final velocities as well as the time interval. In this case, the initial velocity at 0 seconds is 0.0021 m/s and the final velocity at 15 seconds is 0.0083 m/s. The time interval is 15 seconds. So the average vector acceleration is: (0.0083 m/s - 0.0021 m/s)/15s = 0.00028 m/s^2.

## 1. What is the formula for calculating the speed of the tip of the second hand?

The formula for calculating the speed of the tip of the second hand is: speed = (2 * π * radius) / time. The radius is the distance from the center of the clock to the tip of the second hand, and the time is the number of seconds it takes for the second hand to make one full revolution.

## 2. How do you measure the radius of the clock?

The radius of the clock can be measured by using a ruler or a measuring tape to determine the distance from the center of the clock to the tip of the second hand. This distance is typically around 15-20 cm for a standard analog clock.

## 3. What is the time period for the second hand to make one full revolution?

The time period for the second hand to make one full revolution is 60 seconds. This means that the second hand will make 60 revolutions in one hour.

## 4. Is the speed of the tip of the second hand constant?

Yes, the speed of the tip of the second hand is constant. It moves at a constant rate of 1 revolution per minute, regardless of the size or type of clock.

## 5. Can the speed of the tip of the second hand be affected by external factors?

Yes, the speed of the tip of the second hand can be affected by external factors such as the precision of the clock mechanism, temperature, and air resistance. However, these effects are minimal and do not significantly impact the overall speed of the second hand.

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