Displacement & Angle Theta: Figuring Out Centripetal Force

In summary, the conversation discusses the calculation of the angle theta between two points for displacement and the impact of speed on the centripetal force caused by a retracting string. It also mentions that the work done by the pulling string does not affect the angular momentum of the block. Questions are asked about finding tangential speed, the increase in kinetic energy, and the relationship between work done and the kinetic energy. Finally, the speaker mentions that they will not be available for a few hours due to being in the UK.
  • #1
jamiebellend
1
0
Homework Statement
Imagine an object attached to a string kept in circular motion about a fixed point [see picture]. How much work is done between the points rA and rB
Relevant Equations
W=F dot D
For the displacement, how do I figure out the angle theta between the points? And how does the speed at which the string retracts affect the centripetal force?
 

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  • #2
Hi. Pulling code does not affect angular momentum of the block around the center pole. Conservation of angular momentum tells you speed and kinetic energy increased by work done of the block at B.
 
  • #3
Faults in question:
1) Not circular motion - motion will be spiral because r is changing.
2) You are (probably) being asked for the work done by whatever is pulling-in the string; this should have been made clear.

The displacement, angle and centripetal force are not needed (unless you want to make the calculation really hard).

Q1: Can you find the tangential speed at point B? (hint: conservation of angular momenetum)?
Q2: Can you find the increase in the mass's kinetic energy going from A to B?
Q3: How is the work done related to the answer to Q2?

I'm going to bed now (2:21am here in the UK), so won't be posting further for a few hours.
 

1. What is displacement in relation to centripetal force?

Displacement is the distance and direction of an object's change in position. In the context of centripetal force, displacement refers to the change in an object's position as it moves in a circular path.

2. How is displacement calculated for an object in circular motion?

Displacement in circular motion can be calculated using the formula s = rθ, where s is the displacement, r is the radius of the circular path, and θ (theta) is the angle of rotation in radians.

3. What is angle theta and how does it relate to centripetal force?

Angle theta, represented by the symbol θ, is the angle of rotation in a circular path. It is used in the calculation of displacement and is also a key factor in determining the direction of centripetal force, which always acts towards the center of the circular path.

4. How does displacement and angle theta affect centripetal force?

The greater the displacement and angle theta, the greater the centripetal force required to keep an object in circular motion. This is because a larger displacement or angle theta means the object is traveling a longer distance in a shorter amount of time, requiring a stronger force to maintain the circular path.

5. Can displacement and angle theta change during an object's motion in a circular path?

Yes, both displacement and angle theta can change as an object moves in a circular path. This can happen if the object's speed or direction changes, or if the radius of the circular path changes. However, the centripetal force will always act towards the center of the circular path, regardless of any changes in displacement or angle theta.

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