Question

A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is: A. 0.10p m/s2 B. 0.50 m/s2 C. 500p m/s2 D. 1000p2 m/s2 E. 10p2 m/s2

Answer 1

Answer:

2.5 m/s²

Explanation:

Acceleration: This can be defined as the rate of change of velocity.

The S.I unit of acceleration is m/s²

For circular motion, the expression for acceleration is given as,

a = ω²r ................ Equation 1

Where a = acceleration of the particle, ω = angular speed of the particle, r = radius of the circular path.

Given: ω = 5 rev/s = 31.42 rad/s, r = 0.10 m.

Substitute into equation 1

a = 5²(0.10)

a = 25(0.10)

a = 2.5 m/s²

Hence the acceleration of the particle = 2.5 m/s²

Hence, none of the option  is correct

Answer 2

The acceleration of the particle is 98.72m/s²

The formula for calculating the angular acceleration is expressed according to the formula;

$a = \omega^2 r$

where:

$\omega$ is the constant angular speed

r is the radius of the circular path

Given the following parameters:

$\omega$ = 5rev/s = 31.42m/s

r = 0.10m

Substitute the given parameters into the formula:

$a = 31.42^2 \times 0.10\\a=987.2164 \times 0.1\\a= 98.72m/s^2$

Hence the acceleration of the particle is 98.72m/s²

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