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Circular Motion Practice Problems 1. Hal’s favorite disco record has a scratch 12 cm from the center that makes the record skip 45 times each minute. What is the speed of the scratch as it turns in cm/s? v = 56.6 m/s 2. A sock stuck to the inside of the clothes dryer spins around the drum once every 2.0 s at a distance of 0.50 m from the center of the drum. What is the sock’s speed? T = 2.0 s r = 0.50 m v = (2*3.14*r) / T v = (2*3.14 * 0.50) / (2) v = 1.57 m/s 3. What is the radius of an automobile tire that turns with a frequency of 11 Hz and has a speed of 20.0 m/s? v = (2 * 3.14 * r) / T 20.0 = (2*3.14*r) / 0.09 1.8 = 6.28 * r r = 0.28 m 4. A cement mixer of radius 2.5 m turns with a frequency of 0.020 Hz. What is the centripetal acceleration of a small piece of dried cement stuck to the inside wall of the mixer? r = 2.5 m f = 0.020 a=? First find Period: T = 1/f T = 1 / 0.020 T = 50 s Then find velocity: v = (2*3.14*r) / T v = (6.28*2.5) / (50) v = 15.7 / 50 v = 0.314 m/s Then find acceleration a = v^2/r a = (0.314^2) / 2.5 a = 0.039 m/s^2 5. A 70.5 kg pilot is flying a small plane at 30.0 m/s in a circular path with a radius of 100.0 m. Find the magnitude of the force that maintains the circular motion of the pilot. F = ma Find a: Find F: a= v^2 / r F = ma a = (30^2) / 100 F = ( 70.5 * 9) a = 9 m/s^ 2 F = 634.5 N 6. Freddie swings a 2-kg stone at the end of a thin rope of length 1.2 m. He tugs mightily, swinging the stone so fast that the rope is almost horizontal. If the string tension is 200 N, how fast is the stone moving? r = 1.2 m F = 200 N m = 2.0 kg Use F = ma to find acceleration Then, use a = v^2/r to find velocity V = 10.9 m/s 7. The royal antelope of western Africa has an average mass of only 3.2 kg. If this antelope runs with a tangential speed of 9.1 m/s in a circle with a radius of 30.0 m, how large is the force that maintains this circular motion? v = 9.1 m/s r = 30.0 m m = 3.2 kg Find acceleration first. Then find Force using F = ma F = 8.83 N 8. In the Olympic hammer-throw event, an athlete throws a 7.3-kg lead ball attached to a 1.2-m cable. The athlete swings the ball in a circle three or four times before letting it go. If the force of tension in the cable is 4430 N just prior to launch, what is the velocity of the ball? m = 7.3 kg r = 1.2 m F = 4430 N v = 26.9 m/s 9. Shannon sits two meters from the center of a carousel. In 60 seconds, she goes half way around the carousel. What is her speed? r=2m T = 120 s v = (2*3.14*r) / T v = 0.104 m/s