Circular motion and Kinematics

In summary, a boy with a mass of 50kg sits on a chair with a mass of 5kg, which is placed at a distance of 3m from a pole and spins around it with a radial velocity of 1.95 rad/s. The boy drops a ball and the distance from the pole when it hits the ground is calculated to be 4.13m. However, the answer in the book is 12.42m which can be obtained by using ω2r instead of ωr for the initial velocity.
  • #1
Eitan Levy
259
11

Homework Statement


upload_2017-12-18_16-3-19.png

l=2m
b=1.5m
The mass of the chair is 5kg.
A boy with a mass of 50kg sits on the chair.
The distance of the chair from the pole is 3m, and it spins around it horizontally with a radial velocity of 1.95 rad/s.
The boy drops a ball at some moment, what would be its distance from the pole when it hits the ground if the distance of the chair from the ground when it doesn't spin is 0.5m?

Homework Equations

The Attempt at a Solution


First I drew this:
upload_2017-12-18_16-14-51.png

ω2r=v2/r
v=5.85m/s (The velocity of the ball when the boy drops it, all of it horizontal.
Then -1.177=-5t2 (The times it will take the ball to hit the ground).
t=0.4851
Δx=vt=2.8378m
Total distance from the pole: √(3^2+2.8378^2)=4.13m
The answer in the book is 12.42m, I have no idea how they could possible reach to such a large distance.
 

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  • #2
Can you show in detail how you got the initial velocity, 5.85 m/s? It doesn't match the numbers in your figure.
 
  • #3
kuruman said:
Can you show in detail how you got the initial velocity, 5.85 m/s? It doesn't match the numbers in your figure.
It says that the TOTAL distance of the chair from the pole while it spins at this radial velocity is 3m. Therefore r=3m.
 
  • #4
I see. OK, I cannot find anything wrong with your answer. One could get an answer close to the one in the book if one used ω2r for v instead of ωr.
 
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Likes Eitan Levy
  • #5
kuruman said:
I see. OK, I cannot find anything wrong with your answer. One could get an answer close to the one in the book if one used ω2r for v instead of ωr.
Alright, thank you!
 

1. What is circular motion?

Circular motion is the movement of an object in a circular path around a fixed point or axis. It can be uniform, where the object moves at a constant speed, or non-uniform, where the speed and direction of the object change.

2. How is circular motion different from linear motion?

Circular motion involves the movement of an object in a circular path, while linear motion involves the movement of an object in a straight line. In circular motion, the object experiences a centripetal force that keeps it moving in a circular path, whereas in linear motion, there is no such force acting on the object.

3. What is the relationship between circular motion and centripetal acceleration?

In circular motion, the direction of the velocity is constantly changing, which means there is acceleration present. This acceleration is known as centripetal acceleration and is always directed towards the center of the circle. The magnitude of centripetal acceleration can be calculated using the formula a = v^2/r, where v is the velocity and r is the radius of the circle.

4. How do you calculate the period and frequency of an object in circular motion?

The period of an object in circular motion is the time it takes to complete one full revolution around the circle. It can be calculated using the formula T = 2πr/v, where r is the radius of the circle and v is the velocity. The frequency is the number of revolutions per unit time, and can be calculated by taking the reciprocal of the period (f = 1/T).

5. What is the difference between tangential velocity and angular velocity?

Tangential velocity is the speed of an object along its circular path, while angular velocity is the rate at which the object is rotating around the center of the circle. Tangential velocity is measured in units of distance per time (such as meters per second), while angular velocity is measured in units of angle per time (such as radians per second).

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