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.

sinFd

Example 1What 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 3A 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

What is the net torque on the following diagram?

0.5 m =

=1.5 mF2=20 N

F1=20 N

Center of Mass!!!!

EquilibriumFL - FR = 0

FU - FD = 0

ccwcw = 0

Example 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

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

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?

Example

Find the rotational inertia of the following:

m1=3 kg m2=2 kg

L=2.5 m

Example

Find the rotational inertia of the following:

M=2kg

m=4kg

a=1.5 m

b=2 m

Example 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 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.

Example

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/sec2?

Example

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

KER 1

2I 2

Example

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 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

L = Imvr

Example

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

Conservation of Angular Momentum

iI

fi II

Example 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?