University of Texas - PHY 303K

Overton, Mays – Midterm 3

long and has marks every 10 cm, as shown.                                                                                                    

             ABCDEF G

1. F

2. D

3. E

4. A correct

5. B

6. C

2. A 3 kg bicycle wheel rotating at a 2368 rev/min angular velocity has its shaft supported on one side, as shown in the figure. When viewing from the left (from the positive x-axes), one sees that the wheel is rotating in a clockwise manner. The distance from the center of the wheel to the pivot point is 0.6 m. The wheel is a hoop of radius 0.5 m, and its shaft is horizontal.

Assume all of the mass of the system is located at the rim of the bicycle wheel. The acceleration of gravity is 9.8 m/s² .

z

y

x

0.5 m        m g

radius

Find the change in the precession angle after a 1.6 s time interval.

Correct answer: 8.695 ^?.

Explanation:

Let :     m = 3 kg ,

ω = 2368 rev/min

= 2 π (2368 rev/min)

(60 s/min)

= 247.976 rad/s , b = 0.6 m ,   and

R = 0.5 m .

Overton, Mays – Midterm 3 – Due: Apr 6 2005, 10:00 pm – Inst: Turner                                       2

Basic Concepts:

→τ =

d L→ dt

003 (part 1 of 2) 10 points

A small puck of mass 27 g and radius

3. 14 cm slides along an air table with a speed

of 1.7 m/s. It makes a glazing collision with a larger puck of radius 34 cm and mass 66 g (ini- tially at rest) such that their rims just touch. The pucks stick together and spin around af- ter the collision.

Note: The pucks are disks which have a

Using the relation, ?L = τ ?t , where τ

The precession angle ?φ is

?φ = ?L

L

= τ ?t

L

is the

moments of inertia equal to 1 m r².

2

14 cm radius

27 g

L                                                           34 cm

66 g

= m g b ?t m R2 ω

= g b ?t

R2 ω

= (9.8 m/s2) (0.6 m) (1.6 s) (0.5 m)2(247.976 rad/s)

= 0.151756 rad

1. (b)                   (c)

Figure: The two pucks:

1. before they collide,
2. at the time of the collision, and
3. after they collide.

After the collisions the center-of-