Physics 111
Test #5 Formula Sheet
displacement / / angular displacement /
velocity / / angular velocity /
acceleration / / angular acceleration /
constant linear
acceleration
equations / / constant angular acceleration
equations /
mass / m / moment of inertia
(“rotational mass
distribution”) /
force / / torque /
momentum / / angular momentum /
Newton’s 2nd law
Force Impulse
(2nd Law in
integral form) /
/ Newton’s 2nd law – rotational form
Torque Impulse
(2nd Law in
integral form) /
linear kinetic energy / / rotational kinetic energy /
work done by a force / / work done by a torque /
power delivered by force / / power delivered by torque /
Physics 111 – Test #5
1 July 2015
Name ______
Directions: This is a CLOSED BOOK test, and you may only use the calculator and cheat sheet provided. SHOW ALL OF YOUR REASONING! You can only get partial credit for an incorrect answer if you show your reasoning. You may have as much time as you like to finish this exam.
1. (5 pts) Is it possible for a spinning thing to have ω = 0 but have α ≠ 0? If not, prove it. If so, give an example.
2. A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the center of the wheel. The angular speed of the wheel is increasing at a constant rate. Point A is on the rim of the wheel and point B is midway between the rim and center of the wheel (see diagram). For each of the following quantities, is its magnitude larger at point A, at point B, or is it the same at both points? Explain.
a) (5 pts) angular speed
b) (5 pts) tangential speed
3. At t = 5.00 s a point on the rim of a 0.300-m-radius wheel has a tangential speed of 150.0 m/s as the wheel slows down with a tangential acceleration of constant magnitude 45.0 m/s2.
a) (12 pts) Through what angle did the wheel turn between t = 0 and t = 3.00 s?
b) (10 pts) At what time will the radial acceleration of this point on the rim equal g?
4. A gate 4.00 m wide and 2.00 m high weighs 500 N. Its centers of gravity and mass are at its center, and it is hinged at A and B. To relieve the strain on the top hinge, a wire CD is connected as shown in the figure. The tension in CD is increased until the horizontal force at hinge A is zero. Determine
a) (8 points) the tension in the wire CD, and
b) (8 points) the horizontal component of the force at hinge B.
5. (18 points) A bowling ball (mass mb = 5 kg, radius rb = 0.11 m) is attached to a lightweight brace so that the ball rolls down the incline on a fixed axis without slipping. The brace is attached to a rope, which goes over a pulley (mass mp = 1 kg, radius rp = 0.11 m) and is attached to a heavy block (mass M = 10 kg) which sits on a frictional (µk = 0.40) surface. Use ENERGY considerations to determine the speed of the bowling ball after it has rolled from rest 2 m down the incline. Careful! There are several energy terms in your energy equation!
6. (18 pts) An Atwood’s machine is set up as shown in the diagram below. The 50 kg pulley (R = 0.1m) is fixed in place but is free to rotate about an axis through its center. It rotates WITH a frictional torque of 4 Nm. Use torques and forces to determine the tension in BOTH sides of the rope (that’s two different tensions, T1 and T2). (If you ignore the frictional torque, the best you can get is 16/18.)
7. Two solid spheres each with mass 3.00 kg move in the same direction. The radius of each sphere is 10 cm, and they are in deep space, far from any sources of gravity. The top one catches up to the bottom one, and they make a grazing collision, with the bottom of the upper one sticking to the top of the lower one, as shown.
a) (6 points) Determine the velocity of the two stuck-together spheres after the collision (the center of mass velocity).
b) (10 points) Determine the angular velocity () of the two stuck-together spheres after the collision.
BONUS BRAIN BUSTER!!!
A lightweight rod (negligible I) connects two identical point masses, m, forming a dumbbell. It is located in deep space far from any sources of gravity or any other forces. This spins freely in place (the center of mass of the rod/two-mass system isn’t moving) with an angular speed ω about an axis perpendicular to the rod and through its center of mass. Determine an expression for the angular momentum of this dumbbell about the point indicated in terms of m, d, and ω. If you think about it, the answer might surprise you.
Credit will only be given for correct reasoning. If you are able to guess the correct answer but give no correct reasoning, you will receive no extra credit. However, if you give some correct reasoning that would (or does) lead to the correct answer, at least some credit will be given.
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By signing my name above, I affirm that this test represents my work only, without aid from outside sources. In all aspects of this course I perform with honor and integrity.