A particle moves in a circular path of radius 0.15 m with a constant angular speed of 5.0 rev/s. The acceleration of the particle is 986 m/s² 1600 m/s² 0.31 m/s² O 7.5 m/s² O 148 m/s²
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![**Problem Statement:**
A particle moves in a circular path of radius 0.15 m with a constant angular speed of 5.0 revolutions per second. The acceleration of the particle is:
- ○ 986 m/s²
- ○ 1600 m/s²
- ○ 0.31 m/s²
- ○ 7.5 m/s²
- ○ 148 m/s²
**Explanation:**
To find the acceleration of the particle moving in a circular path, we use the formula for centripetal acceleration:
\[ a = \omega^2 \times r \]
where:
- \( \omega \) is the angular speed in radians per second.
- \( r \) is the radius of the circular path.
First, convert the angular speed from revolutions per second to radians per second:
\[ \omega = 5.0 \, \text{rev/s} \times 2\pi \, \text{rad/rev} = 10\pi \, \text{rad/s} \]
Now, use the formula to calculate the acceleration:
\[ a = (10\pi)^2 \times 0.15 \]
\[ a = 100\pi^2 \times 0.15 \]
\[ a ≈ 148 \, \text{m/s}^2 \]
Therefore, the correct answer is 148 m/s².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe073ce94-dbd5-4fb6-b6cc-1f444e07eff5%2F81b8d4a7-2c9e-4770-acf2-9b04570893dc%2Ffyv4ia8_processed.jpeg&w=3840&q=75)
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