Question

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.

Answer 1

Part a)

`\omega = 5 ft/s` counterclockwise

Part b)

`\omega = 2.5 ft/s` counterclockwise

Part c)

`\omega = 2.5 ft/s` clockwise

Step-by-step explanation:

Let the cart has radius R = 1 ft

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

`v_c = 2.5 ft/s`

let the angular speed is given as

`\omega` 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

`v = v_c + r\omega`

`-2.5 = 2.5 + 1(\omega)`

so we have

`\omega = -5 ft/s`

Part b)

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

`v = v_c + 1(\omega)`

`0 = 2.5 + \omega`

`\omega = -2.5 ft/s`

Part c)

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

`5 ft/s = 2.5 ft/s + 1(\omega)`

`\omega = 2.5 ft/s`