A wheel which is initially at rest starts to turn with a constant angular acceleration. After 4 seconds it has made 4 complete revolutions. 1)How many revolutions has it made after 8 seconds

To simplify question, the motion of a point on the wheel along a circular

path is assumed to be at a constant angular rate.

The number of revolution made by the wheel after 8 seconds is = 16

revolutions.

Reasons:

The given parameters are;

The motion of the wheel = Constant angular acceleration.

Number of revolutions made after four seconds = 4

Required:

The number of revolutions made after 8 seconds.

Solution:

The formula for finding the angle turned in an angular motion is similar to

the formula for finding the distance moved in linear motion.

For linear motion, we have;

s = u·t = (1/2)·a·t²

For an angular motion, we have;

θ = ω₀·t + (1/2)·α·t²

Where;

ω₀ = The given initial angular velocity = 0

α = angular acceleration

Therefore, for 4 revolutions, we have;

4×π×2 = 0 × 4 + (1/2) × α × 4² = 8·α

Therefore;

α = π

After 8 seconds, we have;

θ =  0 × 8 + (1/2) × π × 8² = 32·π

The angle turned after 8 seconds = 32·π

1 revolution = 2·π

Therefore;

The number of revolution made by the wheel after 8 seconds is = 16 revolutions.

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16

Step-by-step explanation:

We are given that

Initial velocity,=0

Time=4 s

Number of revolutions in 4 s=4 rev=

Because 1  re= rad

We have to find the number of revolutions made by wheel after 8 s.

Using the formula

Again, t=8

Number of rev=

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step-by-step explanation: