11. Consider two objects whose position vectors are given by r1 and r2 and whose momenta are given by p1 = m1v1 and p2 = m2v2 respectively. Show that in the special case that the center of mass of the two bodies is at rest at the origin (that is P = p1 + p2 = 0, and the position of the center of mass is R = 0), the sum of the angular momenta of the two objects about the center of mass equals the angular momentum of a single object of mass mu = m1m2/(m1+m2), rotating in circular motion about the origin at a distance r = r2-r1. The quantity mu is called the reduced mass.

24. A Pulley system is used to lift a heavy mass. How much force must be applied to lift the object in the attached document aat a steady speed? Neglect friction at the axle.

5. A man of mass 95kg is dancing with his wife, who has a mass of 68kg. Assume that each person's mass is concentrated at their respective centers of mass, which are separated by 48cm.
a. What is the gravitational attraction between them?
b. Which person has the greater gravitational attraction toward the other?

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... Answer : When a net torque is applied to a rigid body ... magnitude of the force that Gina is applying to the ... Gina must apply a force equal to the restoring force ...

... you're doing a problem that uses vectors, velocity) is ... the anthropomorphism -- a force must be applied to change ... for part (a), we simply apply Newton's second ...

... we draw perpendiculars to the two velocity vectors VB and VD ... Torque applied to the disc = τ = FR = 60 x (90 ...Applying the equation ω = ω0 + αt we get: ω = 0 ...

... the spring is unstretched, and the pulley is frictionless ...Applied force F is resolved into components Fcosθ ... Equating the vector sum of vertical forces to zero ...

... As the cable EBF passes over a frictionless pulley, the tension in the same is ... In vector form: ... the block up the slope due to the weight and the applied force P ...

... Tension throughout the rope is assumed to be same as the applied force at one end of the rope. ...Applying the equation s = ut + ½ at2 we get ... The Vector Nature of ...

... it is attached to a second mass, m2 hanging over a pulley. ...Applying the value of a in equation [A ... resultant of all the forces (since force is a vector quantity ...