A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A small blue dot has been painted on the tread of the rear tire. a. What is the angular speed of the tires? b. What is the speed of the blue dot when it is 0.80 m above the road? c. What is the speed of the blue dot when it is 0.40 m above the road?

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Melinda McCombs · Accepted Answer

Given values: 2r=0.8m r=0.4m x1=0.8m υcm=5.6ms a) We will find the angular speed as: ω=υcmr ω=5.6ms0.40m ω=14rads The angular velocity of a point at height x1 will be the sum of the line velocity and the velocity of the center of mass of the wheel. υ=υcm+rω υ=5.6ms+0.4m⋅14rads υ=11.2ms Using the Pythagorean theorem, we have: υ2=(rω)2+υcm2 υ=(rω)2+υcm2 υ=(0.4m⋅14rads)2+(5.6ms)2 υ=7.9195ms a) ω=14rads b) υ=11.2ms c) υ=7.9195ms

Jim Hunt · Accepted Answer

(1) Angular speed =5.60.4=14radianssec⁡, where 0.4m is the radius of the wheel. Since 2n radians is one revolution, 14radianss is 142π=2.23revss or 133.7 rpm. (2) We have to add the tangential speed to the translational speed. The direction is important so we should consider velocity rather than the speed because the tangential velocity is changing but the translational velocity stays the same. At 0.80m the blue dot is at its highest point and the tangential velocity is in the direction of motion=14×0.4=5.6ms. So the speed of the blue dot is 5.6+5.6=11.2ms. (3) The blue dot is 0.4m above the road in two different places. The tangential velocity is vertically upwards or vertically downwards, for the trailing or leading edge of the wheel respectively. The resultant velocity is at an angle of 45° to the road and has a magnitude (speed) of 5.62=7.92ms. This magnitude applies equally to both endpoints of the horizontal diameter. The direction for each velocity is different.

Don Sumner · Accepted Answer

a) d = diameter of tire = 0.80 mr= radius of tire = (0.5) d = (0.5) (0.80) = 0.40 mv = speed of bicycle = 5.6 m/sw = angular speed of the tireSpeed of cycle is given asv=rw5.6=(0.40)ww=14 rad/sb) V′= speed of blue dotaskSpeed blue of dot is given asv′=v+rwv′=5.6+(0.40)(14)v′=11.2 m/sC. here angle b/w both the vectors will be 90 degrees, R=[v2+(rw)2]0.5R=[2∗5.62]0.5R=7.92 m/sec

Eliza Beth13 · Accepted Answer

a) Angular speed (ω) can be calculated using the formula:ω=vrwhere v is the linear velocity and r is the radius of the tire.b) The speed of the blue dot when it is at a certain height above the road can be calculated using the formula:vdot=v2+(r·ω)2where vdot is the speed of the dot, v is the linear velocity, r is the radius of the tire, and ω is the angular speed.Now, let&#039;s solve the problem step by step:a) Angular speed (ω):Given: Diameter of the tire, d=0.80 mRadius of the tire, r=d2=0.802=0.40 mLinear velocity, v=5.6 m/sWe can substitute the given values into the formula to find ω:ω=vr=5.60.40=14rad/sb) Speed of the blue dot at a height of 0.80 m above the road:Given: Height above the road, h=0.80 mWe can substitute the given values into the formula to find vdot:vdot=v2+(r·ω)2=5.62+(0.40·14)2=7.92m/sc) Speed of the blue dot at a height of 0.40 m above the road:Given: Height above the road, h=0.40 mAgain, we can substitute the given values into the formula to find vdot:vdot=v2+(r·ω)2=5.62+(0.40·14)2=7.92m/sTherefore, the speed of the blue dot is *7.92 m/s* at both 0.80 m and 0.40 m above the road.

madeleinejames20 · Accepted Answer

Step 1:a. To find the angular speed of the tires, we can use the formula:{Angular&amp;nbsp;speed}(ω)=Linear&amp;nbsp;speed(v)Radius(r)The radius of the tire is half its diameter, so the radius (r) of the tire is 0.80 m divided by 2, which is 0.40 m. The linear speed (v) of the bicycle is given as 5.6 m/s. Substituting these values into the formula, we get:ω=5.6{m/s}0.40{m}Simplifying the expression gives:ω=14{rad/s}Therefore, the angular speed of the tires is 14 rad/s.Step 2:b. To find the speed of the blue dot when it is 0.80 m above the road, we can use the formula for the linear speed of a point on the circumference of a rotating object:{Linear&amp;nbsp;speed}(v)={Angular&amp;nbsp;speed}(ω)×{Radius}(r)Here, the radius (r) is given as 0.80 m. Substituting the values of ω (14 rad/s) and r (0.80 m) into the formula, we get:v=14{rad/s}×0.80{m}Simplifying the expression gives:v=11.2{m/s}Therefore, the speed of the blue dot when it is 0.80 m above the road is 11.2 m/s.Step 3:c. To find the speed of the blue dot when it is 0.40 m above the road, we can use the same formula as in part (b), but with the new height of 0.40 m. Substituting the values of ω (14 rad/s) and r (0.40 m) into the formula, we get:v=14{rad/s}×0.40{m}Simplifying the expression gives:v=5.6{m/s}Therefore, the speed of the blue dot when it is 0.40 m above the road is 5.6 m/s.

A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A s

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