1. A wheel 30 cm in radius rotates at constant 5 רד/שנייה2. What is the magnitude of the תאוצה לינארית of a point located at (a) 10 cm from the center (b) 20 cm from the center (c) on the edge of the wheel?
ידוע:
Radius (r) = 30 cm = 0.3 m
Angular acceleration (α) = 5 rad/s2
מבוקש: תאוצה לינארית (a) r = 0.1 m (b) r = 0.2 m (c) r = 0.3 m
פתרון:
Relation between linear acceleration (a) and angular acceleration :
a = r α
() linear acceleration, r = 0.1 m
a = (0.1 m)(5 rad/s2) = 0.5 מטר/שנייה2
(ב) linear acceleration, r = 0.2 m
a = (0.2 m)(5 rad/s2) = 1 מטר/שנייה2
(ג) linear acceleration, r = 0.3 m
a = (0.3 m)(5 rad/s2) = 1.5 מטר/שנייה2
2. A pulley 50 cm in radius. If the linear acceleration of a point located on the edge of the pulley is 2 m/s2, determine the angular acceleration of the pulley!
ידוע:
Radius (r) = 50 cm = 0,5 m
linear acceleration (a) = 2 m/s2
מבוקש: the angular acceleration
פתרון:
α = a / r = 2 / 0.5 = 4 rad/s2
3. The blades in a blender 20 cm in radius, initially at rest. After 2 seconds, the blades rotates 10 rad/s. Determine the magnitude of linear acceleration (a) a point located at 10 cm from the center (b) a point located at the edge of the blades.
ידוע:
Radius (r) = 20 cm = 0.2 m
The initial angular velocity (ωo) = 0
The final angular velocity (ωt) = 10 radians/second
מרווח זמן (t) = 2 שניות
מבוקש: the linear acceleration of a point located at (a) r = 0.1 m (b) r = 0.2 m
פתרון:
ωt = ωo + α t
10 = 0 + α (2)
10 = 2 α
α = 10 / 2
α = 5 rad/s
() linear acceleration of r = 0.1 m
a = r α = (0.1 m)(5 rad/s2) = 0.5 מטר/שנייה2
(ב) linear acceleration of r = 0.2 m
a M. 49 α = (0.2 m)(5 rad/s2) = 1 מטר/שנייה2
4. A wheel 20 cm in radius is accelerated for 2 seconds from 20 rad/s to rest. Determine the magnitude of linear acceleration (a) a point located at 10 cm from the center (b) a point located at 10 cm from the center.
ידוע:
Radius (r) = 20 cm = 0.2 m
The initial angular speed (ωo) = 20 rad / s
The final angular speed (ωt) = 0
מרווח זמן (t) = 2 שניות
מבוקש: The linear acceleration (a) r = 0.1 m (b) r = 0.2 m
פתרון:
ωt = ωo + α t
0 = 20 + α (2)
-20 = 2 α
α = -20 / 2
α = -10 rad/s
Negative sign mean the מהירות זוויתית is decrease.
() linear acceleration of r = 0.1 m
a M. 49 α = (0.1 m)(-10 rad/s2) = -1 מטר/שנייה2
(ב) linear acceleration of r = 0.2 m
a = r α = (0.2 m)(-10 rad/s2) = -2 מטר/שנייה2
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