Practice Problems: Uniform Circular Motion
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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/s2. 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 = 4x106 m and 1 day = 100000 seconds.
4. (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 -5.0j 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
5. (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 vo = 2500i + 3000j. One minute later the velocity of the plane is v = -2500i - 3000j. Find the magnitude of the acceleration.
6. (moderate) This problem is not refering to an object in uniform circular motion, but it deals with motion in two dimensions. The velocity of a particle moving in the x-y plane is given by:
v = ( 6.0 t – 4.0 t2 )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?
d. When, if ever, does the speed equal 10.0 m/s?
Please supplement these problems with those found in your companion text.