Calculate the moment of inertia of the system

Question

Assignment:

1. The picture below depicts the trajectory of a pointlike object rotating clockwise at a decreasing speed. Draw at point (A) the direction of: tangent velocity, tangent acceleration, centripetal acceleration and label them clearly as v_t, a_t, a_c.

2. A car initially at rest, free of moving along a track with 8 m radius, is given a constant angular acceleration of 2.5 s^-2 for 4 s. Calculate:

(i) The distance traveled by the car from 0 to 4 s.
(ii) The centripetal acceleration at t = 4 s.

3. Old vinyl records had a radius of 0.15 m and were spinning at 33 RPM. Calculate:

(i) the rotation period.
(ii) the tangent velocity of a point at the edge of the record.

4. In the figure below, the three masses are connected by rigid, massless bars. Calculate the moment of inertia of the system (respect to point (O)).

5. In the figure below:

(i) Calculate the magnitude of the torque of force F respect to the fixed rotation axis.

(ii) Specify the direction of the torque from (i)

6. A solid sphere (I = 2/5 mR²) with mass 2 Kg and radius 0.5 m is initially at rest. The sphere is free to rotate through an axis passing through its center. A force of 10 N is applied at the edge of the sphere, in a direction tangent to the sphere and perpendicular to the rotation axis, for 2 s. Calculate:

(i) The angular acceleration of the sphere.

(ii) The angular speed of the sphere at t = 2 s.