# How To Find Initial Angular Velocity

• rockerdude1210
In summary, the conversation discusses determining the initial angular velocity of a pendulum with an angle function of θ(t)=(0.270rad)cos(4.00t+1.00π). The attempt at a solution using the formula ω=2πf is incorrect as it is only applicable to uniform circular motion, not a pendulum. The correct method is to note that at t=0, the pendulum is at its highest point with zero angular velocity.
rockerdude1210

## Homework Statement

The angle of a pendulum is θ(t)=(0.270rad)cos(4.00t+1.00π), where t is in seconds.
Determine the initial angular velocity.

ω=2πf

## The Attempt at a Solution

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I solved for the frequency, which was 6.37E-1 Hz and subbed it into the formula above and got 4rad/s which is the same ω in the equation but it is wrong. Am I missing something because I can't figure out what is wrong with my method.

The formula ω=2πf is not applicable to this case. That formula is for uniform circular motion, which has constant angular velocity, not for a pendulum, which has variable angular velocity.

From the formula for θ you can deduce that initially (at time t=0) the pendulum is at its highest point, and hence at zero angular velocity.

Ah okay, thanks!

Did you just sub in 0 for t which gave you -0.270 at the θ to figure out that it was at its highest point?

Essentially yes. Cos attains its maximum absolute value at integer multiples of pi.

Makes sense, thank you!

## 1. What is initial angular velocity?

Initial angular velocity is the rate of change of angular displacement with respect to time at the beginning of a rotation. It is usually measured in radians per second (rad/s) or degrees per second (deg/s).

## 2. How do you calculate initial angular velocity?

To calculate initial angular velocity, you can use the formula ω = Δθ/Δt, where ω is the initial angular velocity, Δθ is the change in angular displacement, and Δt is the change in time. Alternatively, you can use the formula ω = 2πf, where f is the frequency of rotation in hertz (Hz).

## 3. What factors affect initial angular velocity?

The initial angular velocity of an object can be affected by several factors, including its moment of inertia, the applied torque, and the distance from the axis of rotation. The shape, size, and mass distribution of the object can also have an impact on its initial angular velocity.

## 4. How can you find initial angular velocity experimentally?

One way to find initial angular velocity experimentally is by using a rotary motion sensor and a data collection system. The sensor measures the angular displacement of the object over time, and the data collection system calculates the initial angular velocity based on this data. Another method is to use a stopwatch and measure the time it takes for the object to complete one rotation, then calculate the initial angular velocity using the formula ω = 2π/t.

## 5. What is the relationship between initial angular velocity and linear velocity?

The relationship between initial angular velocity and linear velocity depends on the distance from the axis of rotation. The linear velocity of a point on a rotating object is equal to the product of the initial angular velocity and the distance from the axis of rotation. This relationship can be expressed as v = ωr, where v is the linear velocity, ω is the initial angular velocity, and r is the distance from the axis of rotation.

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