Question

If the boy on the bicycle in the preceding problem accelerates from rest to a speed of 10.0 m/s in 10.0 s, the angular acceleration of the tires is:_______

Answer 1

The angular acceleration is 3.33 rad/s²

Step-by-step explanation:

Here is the preceding problem as well as the given problem:

A boy rides his bicycle 2.00 km. The wheels have radius 30.0 cm. What is the total angle the tires rotate through during his trip?

21.

If the boy on the bicycle in the preceding problem accelerates from rest to a speed of 10.0 m/s in 10.0 s, what is the angular acceleration of the tires?

Step-by-step explanation:

• To determine the angular acceleration, we will first find the linear acceleration

From one of the equations of kinematics for linear motion

v = u + at

Where v is the final speed

u is the initial speed

a is the linear acceleration

and t is time

From the question, the boy starts from rest, hence,

u = 0.0 m/s

v = 10.0 m/s

t = 10.0 s

a = ??

From, v = u + at

a =
`( v - u)/(t)`

a =
`(10 - 0)/(10)`

a = 1 m/s²

Now, for the angular acceleration,
`\alpha`

The relationship between linear acceleration, a and angular acceleration,
`\alpha` is

a =
`\alpha`r

where r is radius

From the previous question, r = 30.0cm = 0.3m

From the equation, a =
`\alpha`r

`\alpha` = a / r

`\alpha` = 1 / 0.3

`\alpha` = 3.33 rad/s²