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< Mentor Note -- Thread moved from the General Physics forum to HH >

A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9 degrees past the lowest point on its way up, its total acceleration is (-22.5i + 20.2j) m/s^2. For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration\

Attempt at understanding:

I am able to visually picture the system and has been shown in the following link (question #2):

http://facultyfiles.deanza.edu/gems/lunaeduardo/Winter2013Exam1Solutions.PDF

What I don't understand is why the components are being added to find the radial acceleration. Why isn't one of the components simply used to find the radial component. For example, if 22.5 is the horizontal component with an angle for 36.9 degrees with the rope, then why isn't the radial acceleration simply acceleration (radial) = 22.5*cos(36.9).

Unless I am missing some concepts here, please clarify this.

A ball swings counterclockwise in a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9 degrees past the lowest point on its way up, its total acceleration is (-22.5i + 20.2j) m/s^2. For that instant, (a) sketch a vector diagram showing the components of its acceleration, (b) determine the magnitude of its radial acceleration\

Attempt at understanding:

I am able to visually picture the system and has been shown in the following link (question #2):

http://facultyfiles.deanza.edu/gems/lunaeduardo/Winter2013Exam1Solutions.PDF

What I don't understand is why the components are being added to find the radial acceleration. Why isn't one of the components simply used to find the radial component. For example, if 22.5 is the horizontal component with an angle for 36.9 degrees with the rope, then why isn't the radial acceleration simply acceleration (radial) = 22.5*cos(36.9).

Unless I am missing some concepts here, please clarify this.

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