Question

All questions added because it is needed for Question 6 to 11 to be answered (I believe).

Answer Question 6 to 11. Please. Thank you

Practical 3: Rotation due to an External Moment - Pre-Lab Preparation Rotation due to an External Moment: Pre-lab Preparation In this practical exercise you will investigate the angular acceleration of a disc about its centre of mass due to an applied moment, and determine the moment of inertia of the disc. Write down the equation of motion for the disc in terms of its moment of inertia,I, and the tension, T, in the rope, assuming that M0.Recall that the mass and friction of the sensor wheel are negligible. (3) The layout of the apparatus for this practical is shown below St Spindle ep pulley Rotational motion sensor (4) Write down an equation that relates the angular acceleration of the disc and the tangential acceleration at the edge of the stepped pulley. Disc ngr (5) Show that the angular acceleration, α , of the disc is given by α where r is the radius of the step pulley about which the cord is wound. (6) The measurement is repeated times, yieldingn independent values of the average angular acceleration of the disc, all having a similar uncertainty. Write down equations you would use to calculate the mean of these values and the uncertainty in the mean. The mean α values are calculated for various masses m and the dependence plotted. Under what conditions would you expect a linear dependence? Clamp (7) (a) Hanging mass (b) Do you expect the dependence to be linear in the practical? Note that 1 7.5 × 10-3 kg m2 and r 2.5 cm A hanging mass m is suspended by a cord that is wrapped around the step pulley, which is rigidly attached to the disc. The disc can rotate almost freely on a low-friction spindle that passes through its centre of mass. The spindle applies a small kinetic frictional moment, M,, to the disc (c) h is the slope of the line of best fit? (8) Now we include the effect of friction in the spindle. Draw a free-body diagram for the disc showing the tension applied by the cord and the frictional moment. Initially the hanging mass is held stationary. When released, it accelerates downwards, producing a tension in the cord and applying a moment to the disc. (9) Write down the equation of motion for the disc A rotational motion sensor is used to determine the angular acceleration of the disc. The sensor records the time for its wheel to rotate by a fixed angle, from which it calculates the average angular acceleration of the wheel. Since the diameter of the sensor wheel is the same as that of the step pulley, the angular displacement of the sensor wheel and the disc are the same (10) Show that the angular acceleration, α , of the disc is given by α- Assuming M, is independent of m, what should be the effect of the frictional moment on the results? (11) For this practical we were assume that (a) moment of inertia of the sensor wheel is negligible compared to that of the disc, (b) the sensor is frictionless, and (c) the cord does not slip on the sensor wheel. Preparatory work Before coming to the lab you should read the experiment and the relevant sections in your textbook. You should write answers to the following questions on a piece of paper that you bring with you to the laboratory There is no MyUni quiz for this practical, You can obtain help with these questions at the Drop-in Room. (1 Draw a free-body diagram for the hanging mass m (2) Using Newton's second law, write down the equation of motion for the mass.

Answer 1

Free body diagram of hanging mass m, (2) F^rightarrow = m a^rightarrow so, mg - T = ma (3) Top view of disk Since M_f = 0 so, Net torque = I alpha alpha = angular acceleration of disk. Let radius of step pulley be r then, Net torque = T_r = I alpha T_r = I alpha (4) T_r = I alpha T_r = I alpha mg - t = ma so, mg - I_alpha/r = ma alpha = rm(g - a), since there is no slip of rope on step pulley it meet have same angular acceleration should that of pulley that is alpha so its tangential acceleration should be alpha r. the rope is attached to mass m which have acceleration 'a' and rope must be have acceleration equal 'a' so, a = alpha r = alpha = a/r (5) alpha = rm/I (g - a) 1 alpha = rmg - rma