1. Newton’s Second Law for Rotation Examples 1.The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 10 4 kgm 2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s ?

2. Newton’s Second Law for Rotation Examples 1.The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 10 4 kgm 2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s ?

3. Newton’s Second Law for Rotation Examples 1.The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 10 4 kgm 2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s ? Since the force and therefore the torque are constant, the resulting angular acceleration is uniform. Hence, the rotational kinematic equations can be applied.

4. Newton’s Second Law for Rotation Examples 1.The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 10 4 kgm 2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s ?

5. Newton’s Second Law for Rotation Examples 1.The massive shield door at the Lawrence Livermore Laboratory is the world’s heaviest hinged door. The door has a mass of 44 000 kg, a rotational inertia about an axis through its hinges of 8.7 x 10 4 kgm 2, and a width of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and perpendicular to the plane of the door, can move it from rest through an angle of 90.° in 30. s ?

6. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder. 0

7. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder. 0.80 Nm 0 0.72 0.48 -0.80 Nm

8. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder. 0.80 Nm 0 0.48 -0.80 Nm 0.10 0.72

9. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder. 0.80 Nm 0 0.48 -0.80 Nm 0.10 0.14 0.72

10. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder.

11. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder. Units:

12. Newton’s Second Law for Rotation Examples 2.A cylinder having a mass of 2.0 kg can rotate about an axis through its center O. Forces are applied as in the diagram: F 1 = 6.0 N, F 2 = 4.0 N, F 3 = 2.0 N, F 4 = 5.0 N. Also, R 1 = 5.0 cm and R 2 = 12 cm. Calculate the magnitude and direction of the angular acceleration of the cylinder, assuming that during rotation, the forces maintain their same angles relative to the cylinder. Clockwise