CHJ Class activity 1 WEEK I

1. The angular position on a spinning wheel is given by q = t⁴-3t² + 32t +12, where t is in seconds and q is in radians. Determine the following: a) Find the angular position and its velocity at 0, 5, and 10 seconds. b) When is the angular velocity zero? Describe the wheels motion.
   
2. A diver makes 2.5 complete revolutions on the way from a 10.0-m high platform to the water. Assuming zero initial vertical velocity, find the diver’s average angular velocity during a dive.
   
3. At t = 0, a flywheel has an angular velocity of 4.7 rad/s, an angular acceleration of -0.25 rad/s², and a reference line at q_o = 0. a) Through what maximum angle q_max will the reference line turn in the positive direction? b) At what times will the line be at i) q = 1/2 q_max and ii) q = -10.5 rad? Consider both positive and negative values for t.
   
4. A point on the rim of a 0.75-m (diameter) grinding wheel changes speed uniformly from 12 m/s to 25 m/s in 6.2 s. What is its average angular acceleration of the wheel during this interval.
   
5. If an airplane propeller rotates at 2000 rev/min while the airplane flies at a speed of 480 km/h relative to the ground, what is the speed of a point on the tip of the propeller at radius of 1.5m as seen by a) the pilot, and b) an observer on the ground?
   
6. The masses and coordinates of four particles are as follows: 50 g, x = 2.0 cm, y = 2.0 cm; 25 g, x = 0, y = 4.0cm; 25g, x = -3.0cm, y = -3.0 cm; 30g, x = -2.0cm, y = 4.0 cm. What is the rotational inertia of the collection with respect to the a) x, b) y, and c) z axes? d) If the answers to a) and b) are A and B respectively, then what is the answer to c) in terms A and B?
   
7. Two masses m₁ = 0.5 kg and m₂ = 0.6 kg are connected by a massless string over a pulley of radius R and rotational inertia I. The mass of the pulley is 0.20 kg. The string does not slip over the pulley and the table is frictionless. Determine the acceleration of mass m₂.
   
8. Launching herself from a board, a diver changed her angular velocity from zero to 0.620 rad/s in 220 ms. Her rotational inertia is 120 kg.m². a) What was her angular acceleration during the launch? b) What external torque acted on the diver during the launch?
   
9. Determine the Moment of inertia or Rotational inertia for a rigid body consisting of two particles of mass m connected by a rod of length L and of negligible mass under two situations; a) the axis of rotation about the center and b) the axis of rotation at one end of the rod.
   
10. In an Atwood's machine, one block has a mass of 520 g, and the other a mass of 470g. The pulley, which is mounted in a horizontal frictionless bearing, has a radius of 5.50cm. When released from rest, the heavier block is observed to fall 80 cm in 5.00s. a) What is the acceleration of the block? b) What is the tension of the cord that supports the heavier block? c) What is the tension of the cord that supports the lighter block? d) What is the angular acceleration of the pulley? e) What is its rotational inertia?