The cart has a velocity vC = 2.5 ft/sec to the right. Determine the angular speed N (positive if counterclockwise, negative if clockwise) of the wheel so that point A on the top of the rim has a velocity
(a) equal to 2.5 ft/sec to the left,
(b) equal to zero, and
(c) equal to 5.0 ft/sec to the right.

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aristocles aristocles · Answer 1 · 2019-09-20T02:41:31+02:00

Answer:

Part a)

[tex]\omega = 5 ft/s[/tex] counterclockwise

Part b)

[tex]\omega = 2.5 ft/s[/tex] counterclockwise

Part c)

[tex]\omega = 2.5 ft/s[/tex] clockwise

Explanation:

Let the cart has radius R = 1 ft

so here we have speed of the center of the cart is

[tex]v_c = 2.5 ft/s[/tex]

let the angular speed is given as

[tex]\omega[/tex] counter clockwise

Part a)

if the top most point of the rim has same speed as that of speed of the center but it is towards left

so we have

[tex]v = v_c + r\omega[/tex]

[tex]-2.5 = 2.5 + 1(\omega)[/tex]

so we have

[tex]\omega = -5 ft/s[/tex]

Part b)

if the speed of the top point on the rim is zero

[tex]v = v_c + 1(\omega)[/tex]

[tex]0 = 2.5 + \omega[/tex]

[tex]\omega = -2.5 ft/s[/tex]

Part c)

if the speed at the top position on the rim is 5 ft/s

[tex]5 ft/s = 2.5 ft/s + 1(\omega)[/tex]

[tex]\omega = 2.5 ft/s[/tex]