If an object is travelling in circular motion and its period is 3.0 s, how many revolutions will it complete in 1 minute?

1. Break Down the Problem

To find the number of revolutions an object completes in 1 minute, we need to determine how many periods fit into 1 minute.

2. Relevant Concepts

• The period $T$ of an object in circular motion is the time it takes to complete one revolution.
• The number of revolutions per unit time can be calculated as: $\text{Revolutions per second} = \frac{1}{T}$
• To find the total number of revolutions in a specific time (in this case, 1 minute), we can use: $\text{Total Revolutions} = \text{Revolutions per second} \times \text{Total time in seconds}$

3. Analysis and Detail

1. First, convert the period from seconds to revolutions per second: $\text{Revolutions per second} = \frac{1}{3.0 \, \text{s}} \approx 0.3333 \, \text{revolutions per second}$

2. Next, calculate the total time in seconds for 1 minute: $1 \, \text{minute} = 60 \, \text{seconds}$

3. Now, calculate the total number of revolutions in 1 minute: $\text{Total Revolutions} = 0.3333 \, \text{revolutions per second} \times 60 \, \text{seconds} = 20 \, \text{revolutions}$

4. Verify and Summarize

We verified the calculation by ensuring the conversions were correct and both the period and the total time used in the calculation were accurate.

Final Answer

The object will complete 20 revolutions in 1 minute.