Question

An electrical motor spins at a constant 2695.0 rpm. If the armature radius is 7.165 cm, what is the acceleration of the edge of the rotor?

A) 28.20 m/s^2

B) 572,400 m/s^2

C) 281.6 m/s^2

D) 5707 m/s^2

Answer 1

The acceleration of the edge of the rotor is approximately 572400 m/s^2.

Step-by-step explanation:

The acceleration of the edge of the rotor can be determined using the formula:

acceleration = radius x (angular velocity)²

In this case, the radius of the armature is given as 7.165 cm, which is equal to 0.07165 m. The angular velocity can be calculated by converting the given rpm (2695.0) to radians per second. One revolution is equal to 2π radians, and one minute is equal to 60 seconds, so:

angular velocity = (2695.0 rpm) x (2π rad/1 rev) x (1 min/60 s)

Once the angular velocity is determined, it can be substituted into the formula for acceleration along with the radius:

acceleration = (0.07165 m) x [(2695.0 rpm) x (2π rad/1 rev) x (1 min/60 s)]²

Mathematically solving this equation will give the value of the acceleration in m/s². After calculating the expression, we find that the acceleration of the edge of the rotor is approximately 572400 m/s².

Answer 2

Acceleration will be
`5706.77rad/sec^2`

So option (D) will be correct answer

Step-by-step explanation:

We have given angular speed of the electrical motor
`\omega =2695rpm`

We have to change this angular speed in rad/sec for further calculation

So
`\omega =2695rpm=2695* (2\pi )/(60)=282.2197rad/sec`

Armature radius is given r = 7.165 cm = 0.07165 m

We have to find the acceleration of edge of motor

Acceleration is given by
`a=\omega ^2r=282.2197^2* 0.07165=5706.77rad/sec^2`

So acceleration will be
`5706.77rad/sec^2`

So option (D) will be correct answer