A wheel 20cm starts from rest and rotates about horizontal axis through the center with a constant acceleration of 0.5 radian/sec2. A point from the circumference is directly at the right of the center of the wheel. After the end of 2 seconds, find its radial acceleration.A. 15 cm/sec2B. 20 cm/sec2C. 18 cm/sec2D. 19 cm/sec2
Question
A wheel 20cm starts from rest and rotates about horizontal axis through the center with a constant acceleration of 0.5 radian/sec2. A point from the circumference is directly at the right of the center of the wheel. After the end of 2 seconds, find its radial acceleration.A. 15 cm/sec2B. 20 cm/sec2C. 18 cm/sec2D. 19 cm/sec2
Solution
The radial acceleration (also known as centripetal acceleration) of a point on a rotating wheel can be calculated using the formula:
a_r = r * α^2
where:
- a_r is the radial acceleration,
- r is the radius of the wheel, and
- α is the angular acceleration.
Given in the problem, the radius r = 20 cm = 0.2 m (converted from cm to m for consistency in units) and the angular acceleration α = 0.5 rad/sec².
After 2 seconds, the angular acceleration remains the same because it is constant. So, we can substitute the given values into the formula:
a_r = 0.2 m * (0.5 rad/sec²)^2 a_r = 0.2 m * 0.25 sec⁻² a_r = 0.05 m/sec²
However, the answer should be in cm/sec², so we need to convert it back:
a_r = 0.05 m/sec² * 100 cm/m a_r = 5 cm/sec²
None of the provided options (A. 15 cm/sec², B. 20 cm/sec², C. 18 cm/sec², D. 19 cm/sec²) match the calculated radial acceleration. There might be a mistake in the problem or the provided options.
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