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Physics 140 – Homework Week #14       __________Not Due for Marks      10

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Physics 140 – Homework Week #14       __________Not Due for Marks   

 

10.6: Energy in Rotational Motion

1. A uniform wooden meter stick of mass 125 g has a tiny hole drilled at the 75.0 cm mark, and pivots about a nail through the hole.

 

 

When the meter stick is held in the horizontal position, the free end is released, and the meter stick rotates about the pivot. 

 

1. Calculate the moment of inertia of the meter stick relative to the indicated axis of rotation. 
2. Draw a free-body diagram for the bar and identify all forces acting on it. Calculate the net torque acting on the bar. 
3. Calculate the angular acceleration of the bar when it is released. Will it be constant as the bar rotates? Explain. 
4. Determine the angular speed of the meter stick after it has rotated through 90 degrees.

 

2. A 00 kg-textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose mass is 0.80 kg and whose diameter is 0.150 m, to a hanging book with mass 3.00 kg. How fast are the masses moving after the hanging book has descended by 30.0 cm?

 

3. A block of mass 2.0 kg is attached to a string that wraps around a solid pulley of mass 1.0 kg and radius 25.0 cm. If the pulley is initially rotating at 16 rad/s (and the mass is also moving with the pulley), how high does the 2.0 kg mass rise before coming to rest?

 

4. A 5.0-kg, 54-cm-diameter cylinder rotates about an axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the centre of mass at the same height as the axle and then released. Find the magnitude of the cylinder’s angular velocity when it is directly below the axle. 

 

10.7: Static Equilibrium

5. A 110-kg horizontal beam is supported at each end. A 320-kg piano rests a quarter of the way from one end. What is the vertical force exerted by each support on the beam?
6. A 172-cm-tall person lies on a light (massless) board supported by two scales, one under the top of her head, and one beneath her feet. The two scales read, respectively, 35.1 and 31.6 kg. What distance is the centre of gravity of this person from the bottom of her feet? Hint: first determine the person’s weight. 

               

 

 

 

 

7. A shop sign weighing 215 N hangs from the end of a 155-N beam. Find the tension in the supporting wire and the horizontal and vertical forces exerted by the hinge on the beam at the wall. 

 

                     

               

 

 

8. A traffic light hands from a pole as shown in the figure The aluminum pole is 7.20 m long and has a mass of 12.0 kg. The mass of the traffic light is 21.5 kg. Determine…

 

1. The tension in the horizontal, massless cable (CD) and 
2. The vertical and horizontal components of the force exerted by the pivot A on the aluminum pole.  

 

10.8: Angular Momentum

 

9. Determine the magnitude of the angular momentum of the second hand on a clock about an axis through the centre of the clock face. The clock hand has a length of 15.0 cm and a mass of 6.00 g.  

 

10. One of the outcomes of late-stage stellar evolution is that an ordinary star can collapse catastrophically into a neutron star, producing an object with incredibly dense matter. Suppose a star initially has a radius of 7.0 x 10⁸ m (comparable to the sun) and it is initially rotates once every 30.0 days. The star collapses into a neutron star whose final radius is 1.6 x 10⁴ m. Determine the rotation period of the neutron star, assuming that the star’s angular momentum is conserved during this collapse process. 

 

11. A Cirque-du-Soleil performance piece features a large wooden turntable with a mass of 120 kg and a radius of 2.00 m that is initially rotating at 3.00 rad/s about its center. A 70.0 kg trapeze artist then lands on the turntable at a point near the outer edge. Find the angular speed of the turntable after the artist lands.