A car tire of radius 45cm turns at a constant 14 rads/s. For a point on the edge calculate

a) the tangential V
b) the tangential a
c) the centripetal "a"

work:
a) v= rw
v= .45m * 14 rads/s= 6.3m/s
b) at=alphar
alpha= w/t
I am unsure how to get time?
c) at= w^2r
at= 14^2 * .45
at= 88.2 m/s^2

A bike's wheel has a diameter of 70.0cm. If it is rolling at 4.00 revolutions/ s find the forward velocity of the bike (linear motion). Use rotational equations.

d= .35 (after conversion and dividing by 2)
w= 25.12 rads/s (after conversion)

v=rw
v= (.35)(25.12rad/s)= 8.79
did I use the right concept

On the car tire, if the velocity is constant, the tangential acceleration is zero. Right on the other two. I would have done c with v^2/radius.

Yes. The tangential velocity has to be the same as the velocity at the road surface.

Explain Bot Explain Bot answered
8 months ago

Yes, you are correct that for a car tire with a constant velocity, the tangential acceleration is zero. The tangential velocity represents the linear speed at the road surface, so for a point on the edge of the tire, the tangential velocity will be the same as the overall velocity of the car, which in this case is 6.3 m/s.

To calculate the tangential acceleration, you need to know the angular acceleration, which is given by alpha = w/t, where w is the angular velocity and t is the time. Since you are given the angular velocity and not the angular acceleration, you need to know the time component to solve this. However, since the problem states that the car tire is turning at a constant angular velocity, there is no angular acceleration, and therefore the tangential acceleration is also zero.

For the centripetal acceleration, you can use the formula ac = w^2 * r, where w is the angular velocity and r is the radius. Plugging in the values, you correctly calculated the centripetal acceleration as 88.2 m/s^2.

Moving on to the bike's wheel, you correctly converted the diameter to radius by dividing it by 2. The angular velocity is given as 4.00 revolutions per second. To convert this to radians per second, you multiply by 2Ο€, since there are 2Ο€ radians in one revolution. So, the angular velocity is correctly calculated as 25.12 rad/s.

To find the forward velocity (linear motion) of the bike, you can use the formula v = rw, where r is the radius and w is the angular velocity. Plugging in the values, you correctly calculated the forward velocity as 8.79 m/s.

Overall, you used the correct concepts and formulas to solve these problems. Just remember, for a car tire with constant velocity, the tangential acceleration is zero, and for the bike's wheel, the linear velocity is equal to the tangential velocity, which is given by v = rw.

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