A wheel of radius 14 starts from rest and turns through 2.0 revolutions in 3 seconds.?

Question

A) What is its average angular velocity?
B) What is the tangential velocity of a point on the rim of the wheel?

Answer 1

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Angular velocity ω = 2π N where N is the frequency.
Frequency = Number of revolutions / time
Here, the final frequency is [2 /3] = 0.666
Initial frequency = 0.
Average frequency = [1/2] { 0 + 0.666] = 0.333
Angular velocity ω = 2π N where N is the frequency.
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A)
Average angular velocity = 2π N = 2π* 0.333 = 2.094 rad/s
B)
v = r ω
v = 14 *2.094 = 29.32 m/s

Answer 2

It turns pi 14 squared in 3 seconds. So, tangentially, that will be
pi 14 squared /3 per second.

Angular velocity will be 2/3 * 360 = 240 degrees per second.

Got that?

Answer 3

Two turns in 3 sec means ω= 4 * π/3 = 4.18879 Rad/sec.
Tangential velocity = ω * r = 58.64 units/sec
Unit is same as that in which radius is expressed.

Answer 4

A) ω(avg) = 4π/3 ≈ 4.188790 rad./s
B) v = 2*14*4.188790 ≈ 87.96459 units/s