Practice Test 3. Multiple Choice Identify the choice that best completes the statement or answers the question.

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Deborah Hutchinson
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1 Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10.0 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval? a. 95 rad b. 85 rad c. 65 rad d. 75 rad e. 125 rad à d: 75 rad α = Δω Δt = 10 = 2 rad/s1 5 θ = ω f 2 ω i 2 2α = = = 75rad 2. Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.5 m 4.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides? a. 2.2 kg m 2 b. 2.8 kg m 2 c. 2.5 kg m 2 d. 3.1 kg m 2 e. 1.6 kg m 2 à c: 2.5 kg m 2 I = mr 1 = = 2.5kg m 1

2 3. The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30.0 cm, and b = 50.0 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles. a. 2.9 J b. 2.6 J c. 3.1 J d. 3.4 J e. 1.6 J à b: 2.6 J I = mr 1 = = 0.208kgm 1 W = ΔK = K f K i = 1 2 Iω f Iω i 2 = = 2.6J 4. Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars. If the two cars are in line at t = 0, and moving at 3w and w respectively, at what time will they next pass each other? a. t = 0. b. t = p/2w. c. t = p/w. d. t = 3p/w. e. t = 3p/w. à c: p/w. Both cars must rotate to the same angle with one going around one more time. θ = ωt θ + 2π = 3ωt subtract the equations 2π = 2ωt t = π/ω 5. A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. Relative to the positive direction of the axis of rotation, the angular positions of the sphere are positive, its angular velocity is positive, and its angular acceleration is negative. The sphere is a. rotating clockwise and slowing down. b. rotating counterclockwise and slowing down. c. rotating clockwise and speeding up. d. rotating counterclockwise and speeding up. e. first rotating clockwise and then counterclockwise. à b: rotating counterclockwise and slowing down counterclockwise since rotating from the x to the y axis, counterclockwise, is considered positive rotation. Slowing down since it angular acceleration is negative.

3 6. A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction r = ı + ȷ. What is its angular momentum (in kg m 2 /s) relative to the origin? a. 0k b. k6 2 c. -k6 2 d. 6k e. Can t be determined from the information given. à e Can t be determined from the information given. The vector of the direction is not enough. We would need to know close that vector approaches the origin to answer the question. 7. A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is a. (2/3)g b. (1/2)g c. (1/3)g d. (1/6)g e. (5/6)g à (2/3)g This problem can be thought of a rolling down vertical plane. a HI = gsinθ 1 + I mr 1 = g mr1 mr 1 = 2 3 g

8. A solid cylinder rolls without slipping down an incline as shown in the figure. The angular acceleration of the cylinder is. a. (5/7)(g/R) sin q b. (1/2)(g/R) sin q c. (2/3)(g/R) sin q d.

4 8. A solid cylinder rolls without slipping down an incline as shown in the figure. The angular acceleration of the cylinder is. a. (5/7)(g/R) sin q b. (1/2)(g/R) sin q c. (2/3)(g/R) sin q d. (3/5)(g/R) sin q e. (4/5)(g/R) sin q à c: (2/3)(g/R) sin q see previous problem: α = L MN O 9. A force, magnitude F, is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is a. P b. c. S d. T. 1 R. R. 1 R. S R e. 2 R. à d: T S R Considering all the torques and forces F F V = Ma XR F V R FR = Iα The difference here compared to the previous problems is that the force since it is applied at the top of the cylinder also causes a torque. Subtract the equations after multiplying the first equation by R 2FR = Ma XR R + Iα = m = Ma XR R + 1 a 2 MR1 XR R = 3 2 MRa XR a XR = 4 F 3 M

5 10. A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end. In this collision a. momentum is conserved. b. angular momentum is conserved. c. kinetic energy is conserved. d. all of the above are conserved. e. only momentum and angular momentum are conserved. à e only momentum and angular momentum are conserved. momentum and angular momentum are conserved in a collision. Since the objects stick together this is an inelastic collision and kinetic energy is not conserved. 11. A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam? a kn b kn c kn d kn e kn à a: 0.68 kn The pin must exert both a normal force upward to because of the weight of the beam and a force left to balance the normal force of the wall which the beam is leaning against. Considering both the torques and the forces. y: F YZ[ F \ = 0 F Y[ = mg = = 588N x: F Y_` F Z` = 0 Torque: using the pin as the center of rotation LF Yb sin 40 L 2 F \cos40 = 0 F Yb = mg cot40 = cot40 = adding the x and y forces: 680 N

6 12. Aluminum Rod#1 has a length L and a diameter d. Aluminum Rod#2 has a length 2L and a diameter 2d. If Rod#1 is under tension T and Rod#2 is under tension 2T, how do the changes in length of the two rods compare? a. They are the same. b. Rod#1 has double the change in length that Rod#2 has. c. Rod#2 has double the change in length that Rod#1 has. d. Rod#1 has quadruple the change in length that Rod#2 has. e. Rod#2 has quadruple the change in length that Rod#1 has. à a: They are the same Using: L = h = h ij k l m n m j FL L P = π d Y 2F2L L 1 = π d Y = 4FL πd 1 Y = 4FL πd 1 Y 13. Which one of the following cannot be a definition of an elastic modulus? a. V qr qs b. t i ` c. h i h d.v s r e.stress/strain à d: V s r Elastic modulus is defined as stress/strain (e is okay) where stress is F/A which has the units of pressure, P, and, strain is the fractional change in the dimensions of interest and has no units. a, b and c : have the correct units 14. A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of m. What is the magnitude of the gravitational force on the satellite by planet Cruton? a. 63 N b. 58 N c. 68 N d. 73 N e. 50 N à b: 58 N Using F \ = ma H = m v1 r = m 2πr T r 1 = m4π1 R T 1 = 50 4 π1 12 x = 58N

7 15. A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet? a. GmM/(24R) b.gmm/(15r) c.gmm/(12r) d.2gmm/(21r) e.3gmm/(5r) à a: GmM/(24R) The satellite is changing both kinetic and potential energy. The total energy of an orbiting object is: E = 1 2 mv1 GMm r = 1 mv1 r GMm = 1 GMm r 2 r r 2 r 1 GMm = GMm r 2r E = GMm 2 4R GMm 2 3R = GMm 6R GMm 8R = 4GMm 24R 3Mm 24R = Mm 24R 16. Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have a. the smaller period. b. the greater period. c. the smaller gravitational mass. d. the larger gravitational mass. e. the larger universal gravitational constant. à b: a greater period From Kepler s third law: T 1 = K V r S

8 Practice Test 3 Answer Section MULTIPLE CHOICE 1. ANS: D 2. ANS: C 3. ANS: B 4. ANS: C 5. ANS: B 6. ANS: A 7. ANS: A 8. ANS: C 9. ANS: D 10. ANS: E 11. ANS: A 12. ANS: A 13. ANS: D 14. ANS: B 15. ANS: A 16. ANS: B

Practice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.

Practice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Date: _ Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20