Question

A speck of dust on the turntable is at 0.43 rad at t=0 ,What is the angle of the speck at t = 8.1 s ? Your answer should be between 0 and 2π rad Express your answer using two significant figures.

Answer 1

To find the angle of the speck at t = 8.1 seconds, you can use the formula for angular displacement:

θ = θ₀ + ωt

Where:

- θ is the angular displacement (the angle you're trying to find).

- θ₀ is the initial angle (0.43 radians).

- ω is the angular velocity (which we need to calculate).

- t is the time (8.1 seconds).

The angular velocity ω is given by:

ω = Δθ / Δt

Where Δθ is the change in angle and Δt is the change in time. In this case, Δθ is the final angle we want to find (θ) minus the initial angle (θ₀), and Δt is the time interval (t):

ω = (θ - θ₀) / t

Now, plug in the values:

ω = (θ - 0.43 rad) / 8.1 s

Now, solve for θ:

θ = ω * 8.1 s + 0.43 rad

To find θ, you'll need to know the angular velocity ω. If you have this value, you can calculate θ. If not, you won't be able to determine θ accurately without more information about the rotation.