1. Why do we not calculate the torque using the cosine of the angle between r and F?

2. Mathematically, the definition of torque can also be expressed as = (r sin)F In other words, we can always assume thatF, rather than a component of the force, is responsible for rotation. How can this be?

3. A force of 5 N is applied to the end of a a lever that has a length of 2 meters. If the force is applied directly perpendicular to the lever, calculate the magnitude of the torque acting on the lever.

4. A force of 10 N is applied perpendicular to the end of a bar of length 0.2 m. Calculate the torque produced by the force.

5. Marcus is on a merry-go-round holding a string. You are standing next to him and holding the other end of the string so that the string forms a tangent line to the edge of the merry-go-round. If Marcus is 2 meters from the center of the ride, what torque are you applying on him if you pull with 30 N?

6. You have two coins; one is a standard U.S. quarter, and the other is a coin of equal mass and size, but with a hole cut out of the center.

a. Which coin has a higher moment ofinertia?

b. Which coin would have the greater angular momentum if they are both spun at the same angularvelocity?

7. A weight tied to a rope is swung in a circle. The mass of the weight is 2 kg. The weight has a constant speed of 5 m/s and the length of the rope is 1 m. What is the weight's angular momentum?

8. A star is rotating with a period of 10.0 days. It collapses with no loss in mass to a white dwarf with a radius of 0.001 of its original radius.

a. What is its initial angularvelocity?

b. What is its angular velocity after collapse?

9. A merry-go-round consists of a uniformsoliddisc of 225 kg and a radius of 6.0 m. A single 80kg person stands on the edge when it is coasting at 0.20 revolutions per sec. How fast would the device be rotating after the person has walked 3.5 m toward the center.

10. The system pictured in the video above(which includes the student, weights, and spinning seat)has an initial rotational inertiaI_i and an initial angular velocity_i 2.00 rev/s. After the student pulls the weights toward his chest, the final rotational inertia of the system is only 80% of its initial rotational inertia- that is0.800 I_i. Assuming that the angular momentum of the system is conserved, what is the final angular velocity of the system?