Radial acceleration – problems and solutions

1. Which graph below shows the relation between centripetal acceleration or radial acceleration (aR) and linear velocity (v) in uniform circular motion.

Radial acceleration – problems and solutions 1

Solution :

The equation of the radial acceleration :

Radial acceleration – problems and solutions 2

aR = radial acceleration, v = linear velocity, r = distance from the axis of rotation.

We investigate the relation between the radial acceleration (aR) with the linear velocity (v) so that distance from the axis of rotation (r) is constant. For example, r = 1.

Radial acceleration – problems and solutions 3

Graph A.

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2. A ball rotates in a container with a diameter of 1 meter. If the angular speed is 50 rpm, what are the linear velocity and radial acceleration of the ball?

Known :

Diameter of circle (D) = 1 m

Radius of circle (r) = 0,5 m

Angular speed (ω) = 50 rpm = 50 revolutions / 1 minute

1 revolution = 2π radian

50 revolutions = 50 (2π radian) = 100π radian

1 minute = 60 seconds

Angular velocity (ω) = 100π radian / 60 seconds = (10π/6) radian/second

Wanted : Linear speed (v) and radial acceleration (aR)

Solution :

Linear speed (v) :

v = r ω = (0.5)(10π/6) = 5π/6 m/s

Radial acceleration (aR) :

aR = v2/r = (5π/6)2 : 0.5 = 25π2/36 : 0.5 = (25π2/36)(1/0.5)

aR = (25π2/18) m/s2

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3. An object travels at a constant speed v in a circle with radius of R and radial acceleration aR. If the radial acceleration becomes 2 times, then v becomes ………. times and radius becomes ………. times

Solution :

The equation of the radial acceleration :

Radial acceleration problems 4

If the radial acceleration (aR) = 1 then the linear speed (v) = 1 and radius (r) = 1 :

Radial acceleration problems 5

If the radial acceleration (aR) = 2 then the linear speed (v) = 2 and radius (r) = 2 :

Radial acceleration problems 6

If the radial acceleration becomes 2 times, then the linear speed (v) becomes 2 times and the radius of circle becomes 2 times.

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