Physics--Chapter 7: Rotational Motion and the Law of Gravity Supplemental Review Questions (answers at end)

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1 1) A cave dweller rotates a pebble in a sling with a radius of 0.30 m counterclockwise through an arc length of 0.96 m. What is the angular displacement of the pebble? a) 1.6 rad b) 1.6 rad c) 3.2 rad d) 3.2 rad 2) A child sits on a carousel at a distance of 3.5 m from the center and rotates through an arc length of 6.5 m. What is the angular displacement of the child? a) 1.9 rad b) 0.93 rad c) 3.0 rad d) 5.0 rad 3) A bucket on the circumference of a water wheel travels an arc length of 18 m. If the radius of the wheel is 4.1 m, what is the angular displacement of the bucket? a) 1.0 rad b) 4.4 rad c) 3.7 rad d) 2.3 rad 4) What is the approximate angular speed of a wheel rotating at a rate of 5.0 rev/s? a) 3.2 rad/s b) 1.6 rad/s c) 16 rad/s d) 31 rad/s 5) A grinding wheel initially at rest with a radius of 0.15 m rotates until it reaches an angular speed of 12.0 rad/s in 4.0 s. What is the wheel s average angular acceleration? a) 96 rad/s 2 b) 48 rad/s 2 c) 3.0 rad/s 2 d) 0.33 rad/s 2 6) A potter s wheel moves from rest to an angular speed of 0.54 rad/s in 30.0 s. What is the angular acceleration of the wheel? a) 16 rad/s 2 b) 1.3 rad/s 2 c) rad/s 2 d) rad/s 2 7) A record player is turned on and reaches an angular velocity of 4.7 rad/s in 1.37 s. What is the average angular acceleration of the record? a) 3.4 rad/s 2 b) 4.3 rad/s 2 c) 6.4 rad/s 2 d) 0.29 rad/s 2

2 8) A Ferris wheel initially at rest accelerates to a final angular speed of 0.70 rad/s and rotates through an angular displacement of 4.90 rad. What is the Ferris wheel s average angular acceleration? a) 0.10 rad/s 2 b) 0.05 rad/s 2 c) 1.80 rad/s 2 d) 0.60 rad/s 2 9) A Ferris wheel rotates with an initial angular speed of 0.50 rad/s and accelerates over a 7.00 s interval at a rate of rad/s 2. What is the angular speed? a) 0.20 rad/s b) 0.30 rad/s c) 0.46 rad/s d) 0.78 rad/s 10) An automobile tire with a radius of 0.30 m starts at rest and accelerates at an angular speed of 2.0 rad/s 2 for 5.0 s. What is the angular displacement of the tire? a) 12 rad b) 25 rad c) 2.0 rad d) 0.50 rad 11) A bicycle wheel rotates with a constant angular acceleration of 3.0 rad/s 2. If the initial angular speed of the wheel is 1.5 rad/s, what is the angular displacement of the wheel after 4.0 s? a) 6.0 rad b) 24 rad c) 30 rad d) 36 rad 12) A gear in a machine accelerates at 11.2 rad/s 2. If the wheel s initial angular speed is 5.40 rad/s, what is the wheel s angular speed after exactly three full turns? a) 21.2 rad/s b) 13.6 rad/s c) 209 rad/s d) 185 rad/s 13) A ball rolls downhill with an angular speed of 2.5 rad/s and has a constant angular acceleration of 2.0 rad/s 2. If the ball takes 11.5 s to reach the bottom of the hill, what is the final angular speed of the ball? a) 13 rad/s b) 31 rad/s c) 33 rad/s d) 26 rad/s 14) A helicopter has rotor blades 3.0 m long that are rotating at an angular speed of 63 rad/s. What is the tangential speed of each blade tip? a) 99 m/s b) 180 m/s c) 33 m/s d) 66 m/s

3 15) The end of the cord on a weed cutter is 0.15 m in length. If the motor rotates at the rate of 126 rad/s, what is the tangential speed of the end of the cord? a) 628 m/s b) 25 m/s c) 19 m/s d) 63 m/s 16) A point on the rim of a 0.30 m radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.20 m from the center of the same wheel? a) 0.8 m/s b) 1.3 m/s c) 2.6 m/s d) 8.0 m/s 17) A cylinder with a diameter of m rotates in a lathe at a constant angular speed of 35.6 rad/s. What is the tangential speed of the surface of the cylinder? a) 2.67 m/s b) 5.34 m/s c) m/s d) m/s 18) A wheel with a radius of 1.2 m rotates at a constant angular speed of 10.5 rad/s. What is the tangential speed of a point 0.55 m from the wheel s axis? a) 19 m/s b) 5.8 m/s c) 13 m/s d) 8.7 m/s 19) An automobile tire with a radius of 0.3 m accelerates from rest at a constant 2 rad/s 2 over a 5 s interval. What is the tangential component of acceleration for a point on the outer edge of the tire? a) 30 m/s 2 b) 7 m/s 2 c) 0.6 m/s 2 d) 0.3 m/s 2 20) A hamster gets on a stationary wheel with a radius of 0.15 m and runs until the wheel rotates at angular speed of 12.0 rad/s in 4.0 s. What is the tangential acceleration of the wheel s edge? a) 0.45 m/s 2 b) 0.6 m/s 2 c) 1.8 m/s 2 d) 2.9 m/s 2 21) A flywheel with a radius of 0.30 m starts from rest and accelerates with a constant angular acceleration of 0.50 rad/s 2. What is the tangential acceleration of the flywheel? a) 0.63 m/s 2 c) 0.65 m/s 2 b) 0.15 m/s 2 d) 1.30 m/s 2

4 22) A contestant in a game show spins a stationary wheel with a radius of 0.50 m so that it has a constant angular acceleration of 0.40 rad/s 2. What is the tangential acceleration? a) 0.20 m/s 2 b) 0.60 m/s 2 c) 1.3 m/s 2 d) 0.73 m/s 2 23) The tire on a unicycle wheel with a radius of 0.25 m has a centripetal acceleration of 4.0 m/s 2. What is the tire s angular speed? a) 1.0 rad/s b) 2.0 rad/s c) 3.2 rad/s d) 4.0 rad/s 24) A point on the rim of a rotating wheel with a 0.37 m radius has a centripetal acceleration of 19.0 m/s 2. What is the angular speed of the wheel? a) 0.89 rad/s b) 1.6 rad/s c) 7.2 rad/s d) 11 rad/s 25) A lapidary plate at rest is turned on to cut a gemstone. The plate rotates until it reaches an angular speed of 12.0 rad/s in 4.0 s. What is the centripetal acceleration of a point 0.10 m from the center of the plate? a) 0.45 m/s 2 b) 7.2 m/s 2 c) 14 m/s 2 d) 29 m/s 2 26) If the distance from the center of a merry-go-round to the edge is 1.2 m, what centripetal acceleration does a passenger experience when the merry-go-round rotates at an angular speed of 0.50 rad/s? a) 1.7 m/s 2 b) 0.9 m/s 2 c) 0.3 m/s 2 d) 0.6 m/s 2 27) A 80.0 kg passenger is seated 12 m from the center of the loop of a roller coaster. What centripetal force does the passenger experience when the roller coaster reaches an angular speed of 3.14 rad/s? a) N b) N c) N d) N

5 28) A 0.40 kg ball on a 0.50 m string rotates in a circular path in a vertical plane. If the angular speed of the ball at the bottom of the circle is 8.0 rad/s, what is the tension in the string at this point? a) 5.6 N b) 11 N c) 17 N d) 20.0 N 29) A 0.40 kg ball on a 0.50 m string rotates in a circular path in a vertical plane. If a constant angular speed of 8.0 rad/s is maintained, what is the tension in the string when the ball is at the top of the circle? a) 9.0 N b) 11 N c) 13 N d) 10.0 N 30) A roller coaster loaded with passengers has a mass of kg; the radius of curvature of the track at the lowest point of the track is 24 m. If the vehicle has a speed of 18 m/s at this point, what force is exerted on the vehicle by the track? a) N b) N c) N d) N 31) Pizza makers traditionally form the crust by throwing the dough in the air and spinning it. Why does this make the pizza crust bigger? 32) A parent holds a child by the arms and spins around in a circle at a constant speed. If the parent spins fast enough, will the child s feet continue to drag on the ground? Explain your answer. 33) What is the gravitational force between two trucks, each with a mass of kg, that are 2.0 m apart? (G = N m 2 /kg 2 ) a) N b) N c) N d) N 34) The gravitational force between two masses is 36 N. What is the gravitational force if the distance between them is tripled? (G = N m 2 /kg 2 ) a) 4.0 N b) 9.0 N c) 18 N d) 27 N 35) Two small masses that are 10.0 cm apart attract each other with a force of 10.0 N. When they are 5.0 cm apart, these masses will attract each other with what force? (G = N m 2 /kg 2 ) a) 5.0 N b) 2.5 N c) 20.0 N d) 40.0 N

6 36) A 61 kg student sits at a desk 1.25 m away from a 70.0 kg student. What is the magnitude of the gravitational force between the two students? (G = N m 2 /kg 2 ) a) J b) J c) J d) J Answers: 1) c 2) a 3) b 4) d 5) c 6) c 7) a 8) b 9) d 10) b 11) c 12) a 13) d 14) b 15) c 16) c 17) a 18) b 19) c 20) a 21) b 22) a 23) d 24) c 25) c 26) c 27) d 28) c 29) c 30) b 31) Each point on the crust (except the center) has an inertial tendency to move in a straight line. The cohesion of the dough keeps it from flying apart. 32) No, the child s feet will lift off the ground because inertia opposes the force along the child s arm required to keep the child in circular motion. 33) c 34) a 35) d 36)

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