Torque and Rotational Dynamics unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Converting revolutions to radians
Static equilibrium of a beam
Zero net torque does not mean not rotating
A force through the pivot makes no torque
Center of gravity and tipping
What provides the torque in rolling
Tangential vs centripetal acceleration
A couple turns without pushing
Why mass distribution matters
Torque from weight on an extended object
Angular acceleration of a pulley with mass
Common moments of inertia
Short answer 1. Define or explain: Relating linear and angular quantities
3 ptsShort answer 2. Define or explain: Direction of angular velocity
3 ptsShort answer 3. Define or explain: Angular acceleration from torque
3 ptsShort answer 4. Define or explain: Lever arm
3 ptsFree response
10 ptsEXPERIMENTAL DESIGN AND ANALYSIS (Question 3, 10 points). Students investigate balancing systems. A spring scale of negligible mass is fixed to one end of a uniform meterstick whose center is attached to a stand on which it can pivot. A hook of negligible mass on top of a block of mass m0 can be attached through any of several small holes along the meterstick (Figure 1). The students cannot measure m0 directly and cannot attach the block to the spring scale. They must take measurements allowing a linear graph whose slope determines m0. For parts C–D: an identical meterstick of mass M is attached to a frictionless axle fixed to a wall and suspended horizontally by a string connected to a spring scale (Figure 2). The angle θ between string and meterstick can be varied by moving the string among pegs on the wall; the students measure the tension FT needed to hold the meterstick horizontal. Table 1: θ = 22°, 31°, 36°, 45°, 80° with FT = 21, 17, 13, 12, 8 N. The students correctly determine FT = 5Mg/(6 sinθ), and create a graph with 1/sinθ on the horizontal axis.
A. Describe an experimental procedure to collect data that would allow the students to determine m0, including any steps necessary to reduce experimental uncertainty.
B. Describe how the data from part A could be graphed and how that graph would be analyzed to determine m0.
C(i). Indicate what measured or calculated quantity could be plotted on the vertical axis (against 1/sinθ) to yield a linear graph whose slope can be used to calculate M. C(ii). Create the graph: record the plotted values, label the vertical axis with units, and plot the points. C(iii). Draw a straight best-fit line.
D. Using the best-fit line from part C(iii), calculate an experimental value for the mass M of the meterstick.