Old vinyl records had a radius of 015 m and were spinning

Question

Question 1: The picture below depicts the trajectory of a point like 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.

 

Question 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.

Question 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.

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

Question 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).

Question 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.