Radial & Angular Trajectory: Solving for Force

In summary, radial trajectory refers to a straight line path towards or away from a central point, while angular trajectory refers to a curved or circular path around a fixed central point. The trajectory of an object is determined by factors such as initial velocity, angle of launch, and external forces. An object can have both radial and angular trajectory, as seen in objects orbiting around a central point. The trajectory of an object can change over time due to external forces or changes in initial conditions, and real-life examples of radial and angular trajectory include spinning tops and rollercoasters.
  • #1
engineertech0
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Homework Statement



A particle with mass 10kg starts from rest at r = 10 and θ=0 radians, following the trajectory given by r=10-2t , θ=0.2t. Find the radial and angular components and of the force, as functions of time, that will cause this motion


Homework Equations



I am unsure what formulas are needed to solve this equation

The Attempt at a Solution

 
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  • #2
hi engineertech0! :smile:

you are given the path, so you can find the acceleration at time t as a matter of geometry …

then use physics to find the force at time t :wink:
 

1. What is the difference between radial and angular trajectory?

Radial trajectory refers to the path of an object that moves directly away or towards a central point. It can also be described as a straight line trajectory. On the other hand, angular trajectory refers to the path of an object that moves in a circular or curved motion around a fixed central point.

2. How is the trajectory of an object determined?

The trajectory of an object is determined by its initial velocity, angle of launch, and the forces acting upon it, such as gravity and air resistance. These factors can be calculated using mathematical equations and used to predict the path of the object.

3. Can an object have both radial and angular trajectory?

Yes, an object can have both radial and angular trajectory at the same time. This is commonly seen in objects orbiting around a central point, such as planets orbiting around the sun. The object moves in a circular motion (angular trajectory) while also moving away or towards the central point (radial trajectory).

4. How does the trajectory of an object change over time?

The trajectory of an object can change over time due to external forces, such as air resistance, or changes in the object's initial velocity or angle of launch. These changes can cause the object's path to deviate from its original trajectory.

5. What are some real-life examples of radial and angular trajectory?

A spinning top has both radial and angular trajectory, with the top spinning around its central axis (angular trajectory) while also moving in a circular motion (radial trajectory) on a flat surface. A rollercoaster also has both types of trajectory as it moves up and down hills (radial) while also turning and looping (angular).

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