The Conceptual Understanding of Rotationally Dynamic Systems and Their Mechanical Properties
Torque is the rotational analogy of ____?
What is Force?
What is the net torque acting on a rod set against a wall at a 30 degree angle to the horizontal when it is at rest? [I = ML2/3]
What is 0 m N ? ; At rest, the rod has no angular acceleration; therefore, T = Ia = 0.
Points P and Q are 10 meters apart. What is the moment of inertia of point mass P with mass 4kg about point Q? Include units.
What is 400 kg m2 ? The moment of inertia, I, of a point mass is equal to mr2. 4(10)^2 = 400.
If the net torque acting on an object divided by its moment of inertia is equal to 6.2 rad/s2, what is the value of d2(theta)/dt2 ?
What is 6.2 rad/s2 ? The second derivative of angular position is equal to its angular acceleration. The angular acceleration is equal to the given value through T = Ia.
A disc of radius 1m is placed on a frictionless surface and fixed to an axis about its center. There is a CCW torque of 60 m N caused by a force tangent to the edge of the disc. What is the magnitude of this force?
What is 60 N ?
If a wheel has a CW initial angular velocity, and a torque is applied to cause a CW angular acceleration, what happens to the magnitude of the tangential velocity?
What is it increases?
In the diagram, mass A=4kg, B=6kg, C=2kg. Determine the net torque acting on the rod that rotates about its center. Indicate direction.
What is 4 m N CW ?
A penguin is standing at point A on the floor. It then jumps to a height of 1 meter because of its robotic feet. The moment of inertia about point A is (greater/less/the same) at the peak of the jump.
What is greater?
d(theta)/dt = 2t2+5 is used to model a wheel spinning on an axis. What is the angular acceleration of the wheel at time t=5 ?
What is 20 rad/s2
Determine the net torque on the wheel below with radius of 4cm. All applied forces are tangent to the edge of the wheel. Indicate direction.
What is -0.4 m N ? ; The net torque is the sum of r*F*sin(theta). sin(theta) is 1 because of tangency, and opposing forces cancel to yield a 10N force causing a clockwise torque, which is conventionally negative. 10(0.04) = 0.4
A plate is spinning on a frictionless surface when another plate of twice the mass is placed concentrically on top of it. It makes a loud noise as it hits the other plate. What happened to the angular momentum and rotational kinetic energy?
What is momentum is conserved and rotational energy is lost?
A disc of radius 0.5m and mass 3kg is at rest when a force of 30 N is applied tangentially to its edge for 5 seconds. What is the angular speed of the disc after 5 seconds?
What is 25 rad/s ?
Using the parallel axis theorem, determine the change in the magnitude of the moment of inertia of the hoop as the axis of rotation goes from through point A to through point B. The hoop's mass is 1.5kg.
What is 72 kg m2 ?
d2(omega)/dt2 = 8t3+4t+7 is used to model a wheel spinning on an axis. What is the change in angular acceleration of the wheel between time t=0 and time t=1 ?
What is 11 rad/sec2 ?
An 50kg man stands 2 meters above the ground on an 8 meter ladder that is propped against a frictionless wall. The ladder makes an angle of 30 degrees with the horizontal and does not move. What is the torque caused by the man about the point where the ladder contacts the ground?
What is 2000sin(60) m N ?
If two people of equal mass are sitting across from each other on a see-saw at the same distance from the center, where should they sit so that the see-saw has the smallest angular acceleration?
Where is at the end of the seesaw?
2 minute question. A uniform beam of weight 200N and length 4m is attached to a wall. A bird with mass 2kg is sitting on the edge of the beam. The beam is supported by 2 support cables. One support cable is attached halfway along the beam at an angle of 30 degrees to the horizontal and has tension T. Another support cable is attached 1 meter from the wall at an angle of 45 degrees to the horizontal with tension T/(21/2). What is T?
What is 320 N ?
2 minute question. A uniform solid sphere of radius 1m and mass 1kg is centered on an axis of rotation Q. For each meter I move the sphere away, I double its radius but keep the mass density the same. Find the moment of inertia of the sphere about Q when it is 4 meters away. The answer must be numerical but does not need to be simplified. (I = 2/5 MR2)
What is 221/5 + 216 kg m2 ?
A wheel has angular momentum L at time t=0. There is a force applied tangentially at a distance r from the wheel's axis of rotation. This force varies with time according to the equation F = -9t. Calculate the time it takes for the wheel to stop rotating. Express your answer in terms of L and r.
What is root(2L/(9r)) ?
A uniform disc of mass 6kg is initially at rest on top of a ramp of length 18m. The ramp makes a 30 degree angle with the horizontal. The wheel is released to roll down the ramp without slipping. At the instant the wheel reaches the bottom, it has lost one sixth of its initial energy to air resistance. What is the linear speed of the wheel?
What is 10m/s ?
A force is applied to a top that is spinning in free space with angular momentum L. While the force is applied, the direction of the angular momentum changes but the magnitude does not. What must be true about this force?
What is the force is applied perpendicular to the angular momentum?
2 minute question. A horizontal, uniformly distributed rod of mass 4kg is attached to a pole with a pivot such that the rod does not move. Forces acting on the rod are indicated in the diagram. What is the magnitude of the force exerted by the pivot on the arm?
What is 5.86 N?
2 minute question. A solid, uniformly distributed hexagon has area 4(31/2) m2 and moment of inertia given by 5/12 MR2 . Its initial mass is 1kg. A circle concentric with the hexagon and with radius 1 m is then removed from the hexagon. What is its new moment of inertia about its central axis ? (Area of hexagon = (33/2/2) R2 )
What is I = (10/9 - pi/(8*31/2)) kg m2 ?
2 minute question. Find the moment of inertia of the rod about the axis normal to the page at the origin. The mass density is given as a function of r, where r is the distance from the origin. Express your answer only in terms of given constants with correct units.
What is 38 lambda naught kg m2 ?
2 minute question. In the pictured system, mass A with weight 20N and mass B with mass 1kg are attached to a frictionless disc pulley of mass 2kg at their respective heights. The system is then released. What will mass A's kinetic energy be when mass A’s initial gravitational potential energy is equal to the kinetic energy of the entire system?
What is 120 J ?