Lab_6
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1) You spin a wheel to give it an initial angular acceleration. The angular velocity of the wheel decreases with time due to a frictional torque acting on the axle of the wheel. You plot the angular velocity as a function of time. When determining the slope of the linear graph, you measure a change of the angular velocity with a magnitude of rad/s for a time interval of s. What is the magnitude of the angular acceleration due to friction (see Ch8 sheet 5) ? Indicate with positive (negative) sign whether the sign of the measured acceleration is negative (positive).
2) You calculate the moment of inertia of a disk with a handle attached as shown above. The mass of the disk + handle is kg and the radius of the disk is cm. You use the equation in Ch8 sheet 18, which holds for the moment of inertia of a uniform disk, and ignore the handle. What is the moment of inertia ? Indicate with a negative (positive) sign whether you overestimate (underestimate) the moment of inertia of disk + handle, and the error you make is small (large). (Hint: when you judge whether the error made is small or large, consider the mass and the radius of the handle relative to the disk)
3) You measure the moment of inertia of a wheel by measuring its angular acceleration a = rad/s2, when applying an external torque caused by a hanging weight of mass m = 200 g as shown above. The angular acceleration is decreased by a frictional torque, accounted for by afric = - rad/s2 in the expression for the momemt of inertia I of the wheel, I = mr(g-ra) /(|afric|+a), where r is the radius of the cylinder attached to the wheel, and g is the acceleration of gravity, which you treat as error free. You neglect the error of the accelerations a and afric, and the error of the mass m. You find out that the term (a r) in the numerator is small compared to the term g, and thus neglect its error too. What is the absolute error of I, if the 2.5 cm radius r is known with a % accuracy. (Hint: read in the manual of the lab , how I can be written as two factors. One factor contains the quantities assumed to be error free, after taking into account that the term (a r) can be neglected for the purpose of error calculation. Use expression (3) and (4) in "Error and Uncertainty".) Indicate with a positive (negative) sign whether, with the neglections you made above, the absolute (relative) errors of I and r are the same.
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