Question

If a 4kg mass is moving along a circle of radius 0.5m with an angular speed of 100rad/s. find the following.

a. The centripetal acceleration of the particle.
b. The linear speed of the body.
c. The centripetal force acted on the body.

Answer 1

a. The centripetal acceleration is 5000 m/s². b. The linear speed is 50 m/s. c. The centripetal force is 20000N.

Step-by-step explanation:

a. The centripetal acceleration of the particle:

The centripetal acceleration of an object moving in a circle can be calculated using the formula:

ac = rω2

where ac is the centripetal acceleration, r is the radius of the circle, and ω is the angular speed.

Plugging in the values given in the question:

ac = (0.5m)(100rad/s)2 = 5000 m/s2

b. The linear speed of the body:

The linear speed of the body can be calculated using the formula:

v = rω

Plugging in the values given in the question:

v = (0.5m)(100rad/s) = 50m/s

c. The centripetal force acted on the body:

The centripetal force can be calculated using the formula:

Fc = mac

where Fc is the centripetal force, m is the mass, and ac is the centripetal acceleration.

Plugging in the values given in the question:

Fc = (4kg)(5000m/s2) = 20000N