5 Steps to a 5 500 AP Physics Questions to Know by Test Day (2012)
Chapter 8. Rotational Motion (For Physics C Students Only)
211. The study of rotational motion uses what coordinate system?
(A) x, y, z
(B) R, θ, Z
(C) R, θ, Φ
(D) x, θ, Φ
(E) z, θ, Φ
212. What is moment of inertia?
(A) The integral of volume
(B) A function of shape
(C) Resistance to rotation
(D) Rotational equivalent of mass
(E) The integral of volume around the z axis
213. How can one tell if a star has a companion or planet system?
(A) By measuring its rotational energy
(B) By calculating its center of mass
(C) By calculating its center of gravity
(D) By measuring its brightness
(E) By triangulating its distance from Earth
214. Why is a person’s weight greater at the Earth’s equator than at its poles?
(A) This is because the Earth is an oblate spheroid with many mountains near the equator that increase the Earth’s mass.
(B) Heat at the equator expands the person.
(C) The Coriolis effect adds to the weight of gravity.
(D) Cold at the poles makes a person eat more.
(E) The radial component of the Earth’s acceleration adds a slight amount to the gravitational attraction everywhere but the poles.
215. What is Kepler’s first law of planetary motion?
(A) The planets orbit the Sun.
(B) The orbits of the planets are circles with the Sun at the foci.
(C) The orbits of the planets are ellipses with the Sun at one focus.
(D) The orbits of the planets are hyperboloids with the sun at the foci.
(E) The orbits of the planets are all planar.
216. What is the main difference between linear motion and rotational motion?
(A) There are no differences.
(B) One is the analog of the other.
(C) Mass is replaced by the moment of inertia.
(D) Angular momentum is conserved.
(E) The summation of torques is equal to zero.
217. What is the moment of inertia around an axis at the end of a slender bar of mass (m) and length (L) with a large mass (M) of negligible size on its other end? (For a slender rod of mass M, I = ML2 divided by 3.)
(A) I = ML2/3 + ML2
(B) I = mL2/12 + ML2
(C) I = mL2/2 + ML2
(D) I = mL2/3 + ML2
(E) I = mL2/3 + mL2/12
218. Where is the center of mass of a binary star system with a white dwarf star of mass (M) and a Sun-like star of mass (m), separated by a distance (L)?
(A) At R1 = L × (1 - m/(m + M)) from m and R2 = m × L/(m + M) from M.
(B) At R1 = L2 × (1 - m/(m + M)) from m and R2 = m × L2/(m + M) from M.
(C) At R2 = L × (1 - m/(m + M)) from m and R1 = m × L/(m + M) from M.
(D) At R1 = L × (1 + m/(m + M)) from m and R2 = m × L/(m + M) from M.
(E) At R1 = L × (1 - m/(m - M)) from m and R2 = m × L/(m - M) from M.
219. When a skater performs a spin on ice with his arms outstretched, what happens when he brings his arms close to his body?
(A) His angular acceleration decreases because his moment of inertia was decreased.
(B) His angular acceleration increases because his moment of inertia was decreased.
(C) His angular velocity decreases because his moment of inertia was decreased.
(D) His angular velocity increases because his moment of inertia was decreased.
(E) His angular displacement increases because his moment of inertia was decreased.
220. Why must radians be used in rotational motion problems?
(A) Because radians are the unit of displacement
(B) Because radians are based on the properties of a circle, unlike degrees
(C) Because radians make the numbers come out right
(D) Because radians are based on the properties of a rotation, unlike degrees
(E) Radians are an alternative to degrees; either can be used
221. If a ball attached to a string is being twirled in a circle, what happens to the ball if the string is suddenly cut?
(A) The ball curves away from the circle.
(B) The ball curves into the circle.
(C) The ball continues in a circle because of Newton’s first law.
(D) The ball flies off tangent to the circle.
(E) The ball falls to the ground.
222. What is the moment of inertia of a thin-walled cylinder around its central axis?
(A) I = m × R2/2
(B) I = m × R2
(C) I = m × R2/12
(D) I = 2 × m × R2/3
223. What are the angular velocities of the hour hand and the minute hand of Big Ben in the tower of Westminster Palace in London, England?
(A) 1 rph, 1/12 rph
(B) 2π radians/hr, π/6 radians/hr
(C) 1 rpm, 0.08 rpm
(D) π/21,600 radians/s, π/1,200 radians/s
(E) 60 ft/hr, 5 ft/hr
224. A piece of space junk has a mass of 3 kg and is orbiting the Earth every 90 min at an altitude of 300 km. The Earth’s radius is 6.38 × 106 m. What is the junk’s orbital velocity?
(A) 3,710 m/s
(B) 7,420 m/s
(C) 0.001 rad/s
(D) 15,500 m/s
(E) 7,770 m/s
225. What is the kinetic energy of the space junk in Question 224?
(A) 9.06 × 105 J
(B) 23,200 J
(C) 15,500 J
(D) 9.06 × 107 J
(E) 1.81 × 108 J
226. Why is torque a vector?
(A) Because it is the product of a force and a length
(B) Because it is the dot product of a force vector and a length vector
(C) Because it is the cross product of a force vector and a position vector
(D) Because the right-hand rule says so
(E) It is not a vector
227. A proposed “space elevator” would carry materials from the ground to an orbit of 300 km. At what speed would the orbiting platform have to move to keep the elevator perpendicular above the Earth platform?
(A) Speed up the space platform to 6 radians/day
(B) Ensure that the elevator tower is rigid
(C) Speed up the Earth platform to 6 radians/day
(D) Slow the space platform down to 6 radians/day
(E) Slow down the Earth platform to 6 radians/day
228. Newton’s first law states that a body is in equilibrium if the net forces acting on it are zero. How are torques included in this law?
(A) They are not included in the law.
(B) The summation of forces accounts for the forces causing the torques.
(C) The summation of moments accounts for the torques.
(D) Torques are not forces and do not need to be accounted for.
(E) Torques balance each other out and do not need to be accounted for.
229. What happens to the body on which a torque is acting?
(A) Nothing happens to it.
(B) It causes the body to move.
(C) It causes the body to translate.
(D) It causes the body to rotate.
(E) It causes the body to rotate around the axis perpendicular to the torque.
230. When a body is moving in circular motion, what accelerations can be acting on it?
(A) The acceleration vector
(B) Radial acceleration, tangential acceleration, and angular momentum
(C) Radial acceleration, tangential acceleration, and angular acceleration
(D) Radial acceleration, tangential velocity, and angular acceleration
(E) Radial acceleration, tangential acceleration, and angular velocity
231. A car is rounding a flat unbanked curve. At what speed can it go without being thrown from the curve? (Assume the coefficient of friction between the tires and the road is 0.9, the radius of the curve is 50 m, and the mass of the car is 2,000 kg.)
(A) 107 km/hr
(B) 54 m/s
(C) 23 m/hr
(D) 77 km/hr
(E) 77 m/s
232. A bead slides freely and without friction on a circular wire. If the wire is rotated about a diameter, what will happen to the bead?
(A) The bead will stay in its original position.
(B) If the rotational speed is fast enough, the bead will move to a point halfway up the circular wire.
(C) If the rotational speed is too slow, the bead will move to the bottom of the axis of rotation.
(D) Depending on the rotational displacement, the bead will move up the wire.
(E) The bead will reach the top of the wire loop.
233. A race car is speeding on a circular track. It takes 2 min for the race car to finish one circuit of the 1-km radius track. At what speed is the car moving?
(A) 3.14 m/min
(B) 3.14 mph
(C) 3.14 km/s
(D) 3.14 km/min
(E) 3.14 m/s
234. A roller coaster car is moving around a circular loop of the track. At what point is the car’s speed fastest? At what point is the car’s speed the slowest? (Neglect friction.)
(A) Any point on the circle, because the velocities are all the same.
(B) At the bottom of the loop it will be moving the fastest and at the top the slowest.
(C) It is moving at a constant speed, so no point will be faster or slower.
(D) The fastest points will be at 0° and 180°, with the slowest at 90° and 270°.
(E) It is not possible to tell because the car is self-propelled.
235. On a moving Ferris wheel, at what point will a rider’s weight be greatest? At what point will it be the least?
(A) It will be the greatest at 270° and 90° at the least.
(B) The rider’s weight will be the same everywhere on the wheel.
(C) It will be greatest at 180° and 0° at the least.
(D) The rider’s weight will not change.
(E) At the top, it will be the greatest and at the bottom the least.
236. An anchor block of mass (m) is released from rest and is falling through the water to the bottom of the ocean 3 km down. It is attached to a winch of radius (R) and mass (M) by a light, flexible, and strong Kevlar cable. Neglecting drag, the cable’s weight, and slippage on the winch as well as the stretch of the cable, what is the block’s speed when it hits bottom?
(A) ν = ω2 × R
(B) ν = α × R
(E) ν = ω2 × R + α × R
237. What is the moment of inertia of a solid cylinder around an axis parallel to its central axis but along its outside surface?
(A) MR2/2
(B) MR2
(C) MR2/2 + MR2
(D) MR2/12
(E) MR2/3 + 2MR2
238. How much power is a windmill capable of generating in a steady breeze that causes the blades to rotate at 200 rpm? (Assume each of the mill’s three 10-m long blades has a mass of 2,000 kg and neglect all friction losses.)
(A) 2.05 × 106 W
(B) 1.23 × 108 W
(C) 3.26 × 105 W
(D) 6.16 × 106 W
(E) 5.88 × 106 W
239. At a carnival show, one of the booths has a shooting gallery. The idea is to hit the target and knock it over. The guns are loaded with BBs that weigh 0.5 g and have a muzzle velocity of 10 m/s. The targets are 25 cm high and hinged at the bottom. After a target is hit by a BB at 5 cm from its top, what will be its angular velocity just after it is hit? (Assume the target has a moment of inertia of 0.015 kg/m2.)
240. A 2,000-kg car is rounding a banked curve at 170 km/hr. The curve has a radius of 200 m. At what angle must the curve be banked to prevent the car from flying off the curve? (Assume no friction.)