**Practice Problems: Uniform Circular Motion**Click here to see the solutions

1. (moderate) A racecar, moving at a constant tangential speed of 60 m/s, takes one lap around a circular track in 50 seconds. Determine the magnitude of the acceleration of the car.

2. (moderate) An object that moves in uniform circular motion has a centripetal acceleration of 13 m/s^{2}. If the radius of the motion is 0.02 m, what is the frequency of the motion?

3. (easy) Find the centripetal acceleration for an object on the surface of a planet (at the equator) with the following characteristics: radius = r = 4x10^{6} m and 1 day = 100000 seconds.

4.(moderate) For an object in uniform circular motion rank the changes listed

below regarding the effect each would produce on the magnitude of the

centripetal acceleration of the object? Assume all other parameters stay

constant except that noted in the description of the change.

Change A: The speed of the object doubles

Change B: The radius of the motion triples

Change C: The mass of the object triples

Change D: The radius of the motion becomes half as big

Change E: The mass of the object becomes half as big

Change F: The speed of the object becomes half as big

5. (moderate) Outline a procedure by which the centripetal acceleration of a car moving with constant speed on a circular racetrack could be determined. List the standard lab apparatuses needed to make the measurements and the calculations a student can make with the measurements to determine the acceleration. Additionally, determine the range of error introduced into the final answer if each measurement could have an error of 10%. This type of question is very important for your test preparation. Please take your time and answer it completely.

6. (moderate) A particle is moving at a constant speed in a circular trajectory centered on the origin of an xy coordinate system. At one point (x = 4 m, y = 0 m) the particle has a velocity of -5.0**j** m/s. Determine the velocity and acceleration when the particle is at:

a. x = 0, y = -4 m

b. x = -4 m, y = 0

c. x = 0, y = 4 m

d. x = -2.83, y = 2.83 m

7. (moderate) A stunt pilot executes a uniform speed circular path in an airplane. The initial velocity (in m/s) of the plane is given by **v**_{o} = 2500**i** + 3000**j**. One minute later the velocity of the plane is** v** = -2500**i** - 3000**j**. Find the magnitude of the acceleration.

8. (moderate) This problem is not refering to an object in uniform circular motion, but it deals with motion in two dimensions. The velocity (in m/s) of a particle moving in the x-y plane is given by:

v = ( 6.0t – 4.0t^{2})i + 8.0 j

a. What is the acceleration when t = 3.0 seconds?

b. When, if ever, is the acceleration zero?

c. When, if ever, is the speed zero?

**Please supplement these problems with those found in your companion text.**