A wheel accelerates at 1.2 rad /s2 for 24 s. The angular displacement of the wheel is 640 rad during the 24 s. The radius of the wheel is .90 m.

Question

1. What was the final linear speed of a stone caught in the tread of the wheel?
2. What was the linear (tangential) acceleration of a stone caught in the tread of the wheel?
3. What is the final centripetal acceleration of a stone caught in the tread of the wheel?

Answer 1

a). So get linear velocity, the relation is as follows,

v = R*w

where v is linear velocity, w is final angular velocity and R is the radius.

You know the radius but you don't know the final angular velocity.

To get the final angular velocity, the relation is as follows,

w = w_o + α*t

where w is final angular velocity, w_o is the initial velocity, α is the angular acceleration, and t is the time.

We need to find initial angular velocity,

θ = w_o*t + (1/2)α*t

you can find the w_o from the above equation and the you the can find the w and then you can find the v.

b. To find the linear acceleration, use the following relation,

a_t = Rα

c. To find the final centripetal acceleration,

a = v²/R

use the v that you calculated in part a.

Hope it helps, let me know if you have any questions.