UCM and Gravitation Concepts 2

A boy and a girl are riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration? a. Both have zero tangential acceleration. b. There is not enough information given to answer the question. c. the boy d. Both have the same non-zero tangential acceleration. e. the girl

a. Both have zero tangential acceleration. Reason: Both have the same constant angular velocity (change in angle over change in time). Because the angular velocity is constant, the angular acceleration is zero and the tangential acceleration is also zero (tangential acceleration = angular acceleration * radius)

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed? a. They have the same non-zero angular speed. b. There is not enough information given to answer the question. c. Child A d. Child B e. They have the same zero angular speed.

a. They have the same non-zero angular speed Reason: Both children cover the same delta theta (change in angle) over the same period, regardless of their distance from the center. Therefore, they have the same angular speed.

Is it possible for an object moving with a constant speed to accelerate? Explain. a. Yes, although the speed is constant, the direction of the velocity can be changing. b. No, an object can accelerate only if there is a net force acting on it. c. Yes, if an object is moving it can experience acceleration d. No, if the speed is constant then the acceleration is equal to zero.

a. Yes, although the speed is constant, the direction of the velocity can be changing.

The formulas for rotational kinematics have a similar format to those for linear kinematics. Which rotational quantity below is the analog for the linear quantity called velocity? a. w b. ac c. a d. q e. t

a. w Reason: w (omega) corresponds to linear velocity. Linear velocity is change in displacement/change in time, whereas angular velocity is change in angle/change in time.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger centripetal acceleration? a. There is not enough information given to answer the question. b. Child A c. Child B d. They have the same non-zero centripetal acceleration. e. They have the same zero centripetal acceleration.

b. Child A Reason: Centripetal acceleration is v^2/r. Since Child A has the greater linear velocity (v), they also have the greater centripetal acceleration.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular displacement? a. They have the same zero angular displacement. b. They have the same non-zero angular displacement. c. There is not enough information given to answer the question. d. Child B e. Child A

b. They have the same non-zero angular displacement. Reason: Angular displacement is delta theta (change in angle). Since both children experience the same change in angle, they have the same non-zero angular displacement.

A car goes around a curve of radius r at a constant speed v. Then it goes around the same curve at half of the original speed. What is the centripetal force on the car as it goes around the curve for the second time, compared to the first time? a. twice as big b. one-fourth as big c. half as big d. four times as big

b. one-fourth as big Reason: Initial centripetal acceleration = v^2/r Final centripetal acceleration = (v/2)^2/r = v^2/4r = 1/4 * (v^2/r)

A car goes around a curve of radius r at a constant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared to the first? a. one-fourth as big b. twice as big c. one-half as big d. four times as big

b. twice as big Reason: The initial centripetal force = mv^2/r The final centripetal force = m*(2v)^2/2r = 2(mv^2/r)

Two children are on a merry-go-round. Billy is a distance r from the center and Willy is a distance 3r from the center. What is the ratio of Willy's centripetal acceleration to Billy's centripetal acceleration? a. 1/3 b. 9 c. 3 d. 1

c. 3

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that a. Cannot tell which one has the greater angular velocity without knowing their masses. b. Jacques has a greater angular velocity than George. c. both have zero angular velocities. d. Jacques has a smaller angular velocity than George. e. Jacques and George have the same angular velocity.

e. Jacques and George have the same angular velocity. Reason: Regardless of their distance from the center, both Jacques and George experience the same change in angle over the same time period.

Two children of equal mass are on a merry-go-round. Which child experiences the greater centripetal force? a. Impossible to say without knowing the linear speed. b. The child near the center. c. The child near the edge. d. They both have the same centripetal force.

c. The child near the edge. Reason: Centripetal force = mv^2/r. The child closer to the edge has a larger linear velocity than the child near the center, because more distance is being covered over the same time. The child near the edge also has a greater r, but the centripetal force depends more on v because it is raised to the second power. Therefore, the child near the edge has the greater centripetal force.

Which of the following can be a centripetal force? a. friction b. tension c. all of the above d. gravity

c. all of the above Reason: All of the mentioned forces can act as centripetal forces in different situations. Friction - when a car makes a turn, the friction acting on the turned wheels acts as the centripetal force required for circular motion. Tension - when a ball is attached to a string and swung around, the tension in the string acts as a centripetal force by pulling the ball inward in the direction of the center of rotation. Gravity - gravity can act as a centripetal force by pulling planets inwards as they orbit a star.

What force is needed to make an object move in a circle? a. weight b. kinetic friction c. centripetal force d. static friction

c. centripetal force

A ball is whirled on a string, then the string breaks. What causes the ball to move off in a straight line? a. centripetal acceleration b. centrifugal force c. inertia d. centripetal force

c. inertia Reason: The answer is inertia because inertia is the tendency of an object to remain at rest or in motion. In this case, the ball remains in motion with whatever tangential velocity it had just before the string broke.

When an object experiences uniform circular motion, the direction of the net force is a. in the same direction as the motion of the object. b. in the opposite direction of the motion of the object. c. is directed toward the center of the circular path. d. is directed away from the center of the circular path.

c. is directed toward the center of the circular path. Reason: Any object with uniform circular motion has a constant centripetal force acting on it that is directed toward the center of rotation.

Angular velocity is expressed in units of a. omegas per second. b. arcs per second. c. radians per second. d. meters per second.

c. radians per second. Reason: Angular velocity is the change in angle (radians) over the change in time (seconds). Therefore, the units are radians/second.

The formulas for rotational kinematics have a similar format to those for linear kinematics. Which rotational quantity below is the analog for the linear quantity called displacement? a. t b. w c. theta d. a e. ac

c. theta

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger linear displacement? a. They have the same non-zero linear displacement. b. Child B c. There is not enough information given to answer the question. d. Child A e. They have the same zero linear displacement.

d. Child A Reason: Since Child A is at a greater distance from the center than child B, A will travel a greater linear distance (2*pi*r).

The formulas for rotational kinematics have a similar format to those for linear kinemtics. Which rotational quantity below is the analog for the linear quantity called acceleration? a. w (omega) b. ac c. t d. a (alpha) e. q

d. a (alpha)

What is the term for the net force directed toward the center of an object's circular path? a. orbital force b. centrifugal force c. circular force d. centripetal force

d. centripetal force

When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car? a. centripetal force b. centripetal acceleration c. centrifugal force d. inertia

d. inertia Reason: Inertia is the tendency of an object to continue to be in a state of rest or motion. Since the passengers were moving to the right before the left turn, their bodies have inertia and therefore want to keep moving in the right direction even after the left turn has been taken.

Angular acceleration is expressed in units of a. alphas per second squared. b. meters per second squared. c. arcs per second squared. d. radians per second squared.

d. radians per second squared. Reason: Angular acceleration is delta (angular velocity)/delta (time) = (rad/s)/s = radians per second squared.

An object moves in a circle of radius R at constant speed with a period t. If you want to change only the period in order to cut the object's acceleration in half, the new period should be: a. t/4 b. t/2 c. t/sqrt(2) d. t*(sqrt)2 e. 4t

d. t*(sqrt)2

A car goes around a curve of radius r at a constant speed v. What is the direction of the net force on the car? a. toward the back of the car b. toward the front of the car c. away from the curve's center d. toward the curve's center

d. toward the curve's center Reason: Because the car is moving with uniform circular motion, the net force (centripetal force) acts in the direction of the center of rotation.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential acceleration? a. There is not enough information given to answer the question. b. Child B c. They have the same zero centripetal acceleration. d. They have the same non-zero centripetal acceleration. e. Child A

e. Child A Reason: It does not say in the problem that the speed is constant, which implies that the merry-go-round is accelerating. This means that Child A has the greater tangential acceleration because they are further from the center of the merry-go-round and tangential acceleration = angular acceleration * distance from center.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed? a. Child B b. They have the same non-zero tangential speed. c. They have the same zero tangential speed. d. There is not enough information given to answer the question. e. Child A

e. Child A Reason: Although they have the same angular velocity, Child A is at a greater distance from the center of the circle than child B. Therefore, Child A's tangential speed will be greater because tangential speed = angular velocity * distance from the center of the circle.

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that a. Jacques and George have the same tangential speed. b. Jacques has a greater tangential speed than George. c. both have zero tangential speeds. d. Cannot tell which one has the greater speed without knowing their masses. e. Jacques has a smaller tangential speed than George.

e. Jacques has a smaller tangential speed than George. Reason: This is true because Jacques is closer to the center of the merry-go-round than George and tangential speed = angular speed * distance from the center.