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A turntable reaches an angular speed of 33.3 rpm in 2.04 s, starting from rest. Assuming the angular acceleration is constant, what is its magnitude? How many revolutions does the turntable make during this time interval? Do not enter unit.

Question

A turntable reaches an angular speed of 33.3 rpm in 2.04 s, starting from rest. Assuming the angular acceleration is constant, what is its magnitude? How many revolutions does the turntable make during this time interval? Do not enter unit.

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Solution

To solve this problem, we need to use the equations of rotational motion.

Step 1: Convert the angular speed from revolutions per minute (rpm) to radians per second.

1 revolution = 2π radians and 1 minute = 60 seconds.

So, 33.3 rpm = 33.3 * 2π / 60 = 3.49 rad/s.

Step 2: Calculate the angular acceleration.

The formula for angular acceleration (α) is change in angular velocity (ω) divided by change in time (t).

The turntable starts from rest, so the initial angular velocity is 0.

Therefore, α = (ω - 0) / t = 3.49 rad/s / 2.04 s = 1.71 rad/s².

Step 3: Calculate the number of revolutions.

The formula for angular displacement (θ) is initial angular velocity (ω₀) times time (t) plus 0.5 times angular acceleration (α) times time squared (t²).

Since the turntable starts from rest, ω₀ = 0, and the formula simplifies to θ = 0.5 * α * t².

Substituting the given values, θ = 0.5 * 1.71 rad/s² * (2.04 s)² = 3.57 rad.

To convert this to revolutions, divide by 2π: 3.57 rad / 2π = 0.57 revolutions.

So, the angular acceleration is 1.71 rad/s² and the turntable makes 0.57 revolutions.

This problem has been solved

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