Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Circular Motion

Assume a bird completes a circle of radius 8.00m every 5.00s and rises vertically at a rate of 3.00 m/s

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Ok so I was able to find the acceleration which is 12.6 m/s^2 and the velocity which is 10.5 m/s.

However, Im asked to find the direction of the bird's acceleration and the angle between the bird's velocity vector and horizontal....and im not sure how to do that?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Circular Motion

the centripetal part of the acceleration keeping it moving in a circle is

a = w²r = 8×(2π/5)² = 12.6ms-² (what you got)

since its rising vertically at a constant speed, its vertical acceleration is 0. so only the centripetal acceleration acts.
the centripetal acceleration acts towards the centre of rotation, in the horizontal plane - theres nothing more you can say.

v = wr = 10.1ms-¹ (to 4sf its 10.05, so 10.1 not 10.5)

that part of the velocity acts in the horizontal, you then have the 3ms-¹ acting upwards, so you could see it as a right angled triangle. the 10.1 as the base, and 3.00 as the elevation, giving the angle between horizontal and velocity as tan-¹(3.00/10.1) = 16.5°

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