Problems with velocity/acceleration involving clock arm

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In summary, the traditional watch has a second hand that is 2.0 cm long from the center to the tip. Using the sine law and SOH CAH TOA, the speed of the tip of the second hand is calculated to be 0.3 cm/s. Using the cosine law, the velocity at 20s can be found to be 2 cm, but the calculations for 40s and 60s are incomplete. The difference in velocity between 15s and 30s is unknown. The distance traveled by the tip of the second hand in 60 seconds is also unknown.
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Homework Statement


A traditional watch has a second hand 2.0 cm long, from centre to tip

a. what is the speed of the tip of the second hand?
b. What is the velocity of the tip at 20s? 40s? and 60s?
c. What is it's change in velocity between 15s and 30s?
d. What is it's average acceleration durning the same time interval


Homework Equations


d = v * t
sine law
cosine law
SOH CAH TOA

The Attempt at a Solution


a) used SOH CAH TOA to find the third side of the 90 degree (clock) triangle
cos45 = 2/h
cos45h = 2
h = 4cm (rounded)

v = d/t
v = 4cm / 15s
v = 0.3cm/s

therefore the velocity of the clock arm is 0.3cm/s
****attached is the clock and the final 90 degree triangle****

b) I used the cosine law to TRY to find the other side
due to the clock being on 20s the angle from the start to the ending point of 20s is 120 degrees

C^2 = A^2 + b^2 - 2(2)(2)cos120
c^2 = 8 - 4
C^2 = 4
C = 2

this is where I got stuck
****there is an attachment of the triangle I drew****

thanks to anyone willing to help :D
 

Attachments

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    traingle.png
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  • clock.png
    clock.png
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  • #2
What is the difference between speed and velocity?
 
  • #3
the only difference I really see would be that a velocity is a vector while speed is a scalar.
 
  • #4
What is important is the actual distance that the tip of the second hand travels, not the distance between one location and another (which is displacement, not distance traveled).
 
  • #5
I'm still pretty confused on how to do it :/
 
  • #6
bump
(come on I need lots of help!)
 
  • #7
How far does the tip of the second hand travel in 60 seconds?
 

Related to Problems with velocity/acceleration involving clock arm

1. What is the equation for velocity/acceleration involving clock arm?

The equation for velocity is v = rω, where v is the linear velocity, r is the radius of the clock arm, and ω is the angular velocity. The equation for acceleration is a = rω², where a is the linear acceleration and ω is the angular acceleration.

2. How does the length of the clock arm affect the velocity/acceleration?

The length of the clock arm affects the velocity and acceleration in a direct manner. As the length of the arm increases, both the linear and angular velocity also increase. Similarly, a longer arm will result in a higher linear and angular acceleration.

3. Can the direction of the clock arm affect the velocity/acceleration?

Yes, the direction of the clock arm can affect the velocity and acceleration. The linear velocity is always tangential to the circular path of the arm, while the angular velocity is perpendicular to the plane of the arm. Therefore, changing the direction of the arm will alter the velocity and acceleration values.

4. How do you calculate the linear and angular velocity from the clock arm's position?

The linear velocity can be calculated by dividing the change in the position of the clock arm by the change in time. The angular velocity can be calculated by dividing the change in the angle of the arm by the change in time. Both of these calculations require the use of a reference point and the units should be consistent (e.g. meters and seconds).

5. What are some real-world applications of problems with velocity/acceleration involving clock arm?

Problems involving velocity and acceleration of a clock arm have various real-world applications, such as timekeeping devices, pendulum clocks, and mechanical clocks. These calculations are also important in fields such as physics, engineering, and robotics. Additionally, understanding the velocity and acceleration of the clock arm can help in designing more accurate and efficient timekeeping mechanisms.

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