Question
A blue sphere and a red sphere with the same diameter are released from rest at the top of a ramp. The red sphere takes a longer time to reach the bottom of the ramp. The spheres are then rolled off a horizontal table at the same time with the same speed and fall freely to the floor. Which sphere reaches the floor first?
(A) The red sphere
(B) The blue sphere
(C) The sphere with the greater mass
(D) Neither; the spheres reach the floor at the same time.
▶️Answer/Explanation
Ans:C
Question
A friend is balancing a fork on one finger. Which of the following are correct explanations of how he accomplishes this? Select two answers.
(A) Total energy is conserved.
(B) The fork’s moment of inertia is zero.
(C) The fork’s center of mass is above his finger.
(D) The fork’s clockwise torque is equal to its counterclockwise torque.
▶️Answer/Explanation
Ans: (C) and (D)
An object’s center of mass is the balancing point by definition. The reason for this is that the moment arm on one side is the same as on the other. Therefore, the torque caused by gravity on either side will cancel.
Question
An object is experiencing a nonzero net force. Which of the following statements is most accurate?
(A) The linear and angular momentums of the object are both definitely changing.
(B) Although the linear momentum of the object is definitely changing, the angular momentum may not be.
(C) Although the angular momentum of the object is definitely changing, the linear momentum may not be.
(D) Neither the linear momentum nor the angular momentum is definitely changing.
▶️Answer/Explanation
Ans:(B)
Since \(F\Delta t=\Delta p\), net force will change the linear momentum. However, torque also involves the lever arm \((\tau=RF\sin\Theta)\). So despite having a nonzero net force, the net torque might still be zero.
Question
What is the net torque acting on the pivot supporting a 10-kilogram beam 2 meters long as shown above?
(A) 198 N · m
(B) − 198 N · m
(C) − 102 N · m
(D) 102 N · m
▶️Answer/Explanation
Ans:( C )
Take the center of mass to be 1 meter from the pivot:
Net Torque = \(+mg(1)\sin90^{\circ}-200(2)\sin30^{\circ}\)
\(=98-200=-102N\cdot m\)
Question
An old record player could bring a disk up to its 45 RPM speed in less than a second. If the same size disk can also be brought up to a speed of 75 RPM in about the same amount of time on another player, compare the two torques.
(A) The torques would be the same as the moment of inertia of the two disks are the same.
(B) The torques would be the same because of the conservation of angular momentum.
(C) The torque would be larger in the second case as it requires a greater angular acceleration.
(D) The torque would be larger in the second case as it entails both a larger force and a larger lever arm.
▶️Answer/Explanation
Ans:(C)
Torque = \(I\alpha\)
\( \alpha=\) angular acceleration =\(\Delta\omega/\Delta t\)
Our only data provided are that the angular acceleration must be larger for the 75 RPM record and that the moment of inertia has not changed (same disk). Therefore, the torque supplied must be larger.
Question
Which of the following must be zero if an object is spinning at a constant rate? Select two answers.
(A) Net torque
(B) Moment of inertia
(C) Angular momentum
(D) Angular acceleration
▶️Answer/Explanation
Ans:
(A) and (D) Constant angular velocity means zero angular acceleration, which means no net torque.