CP Physics Chapter 8 Rotational Dynamics

Torque --Torque is the quantity that measures the ability of a force to rotate an object around some axis.

Example 1 What is the torque produced by a 100 N force applied to a door at the doorknob that is located 0.85 m from the hinges?

Example 2 This time the force is applied at a 35 degree angle with the door from example #1

Example 3 A basketball is being pushed by two players during tip-off. One player exerts a downward force of 11 N at a distance of 7.0 cm from the axis of rotation. The second player applies an upward force of 15 N at a perpendicular distance of 14 cm from the axis of rotation. Find the net torque acting on the ball.

Example 4 What is the net torque on the following diagram? 0.5 m = =1.5 m F2=20 N F1=20 N

Center of Mass!

Equilibrium  F L -  F R = 0  F U -  F D = 0  ccw  cw = 0

Example 5 How far from the end of a 5 m see-saw must a 35 kg kid sit if his 45 kg older sister is sitting 1.1 m from the other end? What is the force the fulcrum exerts on the see-saw if the board is 4 kg?

Example 6 A 4 kg, 3 m see-saw is off center 0.25 m. If a 35 kg boy sits 0.5 m from the end on the short side, where must his older 45 kg sister sit in relation to the opposite end?

Example 7 An 80 kg man is on a 18 kg scaffold supported by a cable on each end. If the man is standing 1.68 m from one end of the 6 m long scaffold, what is the tension in each cable?

Rotational Inertia Downhill Race  Two objects, a solid disk & a ring, are in a downhill rolling race.  They have equal mass & diameter.  Which object wins??

Rotational Inertia / Moment of Inertia Linear inertia describes an object’s resistance to changes in linear motion.  Depends on mass; more mass = more inertia Rotational inertia describes an object’s resistance to change in rotational motion.  It’s easier to rotate an object around some axes than others, even though the mass has not changed.  Depends on mass & mass distribution.  This is called Moment of Inertia. This is the rotational counterpart to mass.

Example 8 Find the rotational inertia of the following: m 1 =3 kg m 2 =2 kg L=2.5 m

Example 9 Find the rotational inertia of the following: M=2kg m=4kg a=1.5 m b=2 m

Example 10 What is the rotational inertia of a 5 kg rod that is 2.0 m long and rotates around an axis through its center and perpendicular to the bar.

Example 11 What is the rotational inertia of a 0.45 m diameter bowling ball with a weight of 71.2 N that spins about an axis through its center.

Newton’s Second Law for Rotation becomes

Example 12 What is the torque produced by a whirling a 3 kg rock on a 1.1 m long string with an acceleration of 38 m/sec 2 ?

Example 13 A 2.2 m long board is fixed to rotate at one end. It is held horizontal and then released. A. What is the angular acceleration of the board upon release? B. What is the tangential acceleration of the end of the board upon release?

Rotational Kinetic Energy becomes

Example 14 A 13.5 kg thin ring with a radius of 33 cm, respectively rolls across a table at 5.7 m/sec. How much total kinetic energy does the ring have?

Example 15 A basketball starts from rest at the top of a 7 m long incline of 30 degrees. How fast is it moving at the bottom of the hill using the conservation of energy?

Angular Momentum, L becomes… OR

Example 16 A 48 kg kid is on a 19 kg merry-go- round rotating at 7 rad/sec and is located 1.6 m from the edge of the 5 m diameter disk. What is the angular momentum of the system?

Conservation of Angular Momentum Figure Skating

Example 17 A 25 kg merry-go-round rotates at 0.2 rev/sec with an 80 kg man standing on the rim of the 4 m diameter disk. How fast is it rotating if the man moves to 0.5 m from the center of the disk?