Question 1: A particle of mass m=1kg has position vector T (t) given by T(t) = Ati + Bt²j+Ct³k (meters) where A, B, and C are constants. At t=1 second, find a) the torque, 7, with respect to the origin, and b) the angular momentum, L, with respect to the origin.

A planet is at a position of r→=3.0×10^12mx̂ − 4.0×10^12mŷ as it moves in an elliptical orbit around a large star at the origin (x=0, y=0).  If the planet has a mass of 6.0 ×1026 kg and is moving with a velocity of v→=9.5km/sx̂, what is its angular momentum vector?  (give magnitude and direction)

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In the figure, a 0.400 kg ball is shot directly upward at initial speed 51.9 m/s. What is the magnitude of its angular momentum about P, 6.03 m horizontally from the launch point, when the ball is (a) at maximum height and (b) halfway back to the ground? What is the magnitude of the torque on the ball about P due to the gravitational force when the ball is (c) at maximum height and (d) halfway back to the ground? Ball (a) Number Units (b) Number Units (c) Number Units (d) Number Units

An object of mass 2.75 kg is moving with a velocity v = (3.8of – 5.10k) m/s. What is the angular momentum of the mass relative to the origin when it is at the location (1.50, -1.50, 1.50) m? (Express your answer in vrector form )

An ice skater is spinning at 5.4 rev/s and has a moment of inertia of 0.44 kg ⋅ m2. Part (a)  Calculate the angular momentum, in kilogram meters squared per second, of the ice skater spinning at 5.4 rev/s.  Part (b)  He reduces his rate of rotation by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia (in kilogram meters squared) if his rate of rotation decreases to 0.75 rev/s. Part (c)  Suppose instead he keeps his arms in and allows friction of the ice to slow him to 3.25 rev/s. What is the magnitude of the average torque that was exerted, in N ⋅ m, if this takes 17 s?

A 7.33 kg particle with velocity (1.80 m/s)i (6.97 m/s ) is at x = 5.08 m, y = 3.64 m. It is pulled by a 5.87 N force in the negative x direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing? (a) Number i (b) Number (c) Number I i = k Units k Units k Units >