A sphere or cylinder with mass M and radius R is rolling down a ramp. Use the sketch to answer the following questions:
1) [(lab manual Eq. (10))] There are two marks on the ramp that are 1 meter apart. If it takes 2.7 seconds to roll from the 1st mark to the 2nd mark, what is the measured acceleration?
2) If all you have is a ruler and calculator, show measurements would you take to measure sin(̑̑θ) on the sketch and write the equation sin(θ) = __________. To minimize error, make sure your measurements make a right triangle (don't chop off a corner).
Fill out the table below with the answers to the following questions using g = 9.8 m/s²:
3) [lab manual Eq. (3), Ch. 7.5 Table 7.1 for Icm] Write an equation in terms of mass M and radius R for the moment of inertia of the center of mass Icm and for the effective moment of inertia Ieffective for the object shapes in the table. The first row is done as an example for you.
4) [lab manual Eqs. (6) to (9)] Write a formula for the objects' acceleration in terms of g and θ.
5) If θ = 2.4° = 0.042 radians, what is the acceleration for each object? Watch your angle units!