Question

Part A:

Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second?

____ rev/s

What is the angular velocity in radians per second?

____ rad/s

Part B:

A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher's hand is 32.0 m/s and the ball is 0.220 m from the elbow joint, what is the angular velocity (in rad/s) of the forearm?

_______rad/s

Part C

An ordinary workshop grindstone has a radius of 8.00 cm and rotates at 6000 rev/min.

(a)

Calculate the magnitude of the centripetal acceleration at its edge in meters per second squared and convert it to multiples of g.

magnitude_____ m/s²

magnitude____ g

(b)

What is the linear speed in m/s of a point on its edge?

______ m/s

Answer 1

Part A -

Angular velocity, w = 6 rev/min = 6 / 60 rev/s = 0.10 rev/s

Convert this in rad/s -

w = 0.10 * 2*pi = 0.63 rad/s

Part B -

Here, linear velocity, v = 32.0 m/s

Radius, r = 0.220 m

Hence, angular velocity, w = v / r = 32.0 / 0.22 = 145.4 rad/s

Part C -

(a) Angular velocity, w = 6000 rev/min = (6000*2*pi) / 60 rad/s = 628.2 rad/s

So, magnitude of centripetal acceleration = w^2*r = 628.2^2 * 0.08 = 31571 m/s^2

Compare this value with gravitational acceleration -

a = 31571 / 9.8 = 3221g

(b) Linear velocity of a point at the edge, v = r*w = 0.08*628.2 = 50.3 m/s