What is the drill’s angular acceleration?

A high-speed drill reaches 2,000 rpm in 0.50 s. What is the drill�s angular acceleration? Through how many revolutions does it turn during this first 0.50 s?

Answer

General guidance

Concepts and reason
The concept of angular acceleration and rotational kinematic equation is used here. First, convert the value of angular velocity from rpm to rad/s. Substitute the value of in the angular acceleration expression and find the result. In the next part, use the rotational kinematic equation برزand find the number of revolutions.

Fundamentals

The expression of the angular acceleration is given as follows: Here, is the angular velocity and t is the time. The number of revolutions made by the drill in first 0.5 s is calculated as: برز Here, is the angular acceleration and t is the time.

Step-by-step

Step 1 of 2

(a) Convert the value of angular velocity from rpm to rad/s. @= 2000 rpm( 27 rad
pm rev | 605
1 m
= 206 rad/s Substitute 206 rad/s for and 0.5 s for t in the expression . a
206 rad/s
=
0.5 s
= 418 rad/s?

Part a

The angular acceleration of drill is 418 rad/s?.


For the angular acceleration, use the expression of angular acceleration, substitute the value of angular velocity and time in the expression and find the result.

Step 2 of 2

(b) Substitute 418 rad/s? for and 0.5 s for t in the expression برز. 0 = (418 rad/s?)(0.5 s)
= 52.25 rad Convert the value of from rad to revolutions.

0 = 52.25 rad( 1 revolution
rad
21
= 8.32 revolutions

Part b

The number of revolutions made by drill is 0.5 sec is 8.32 revolutions.


Use the angular acceleration value calculated in the above part to find the number of revolutions. Since, the wheel makes rad in one revolution. Hence, divide the value of by and calculate the number of revolutions.

Answer

Part a

The angular acceleration of drill is 418 rad/s?.

Part b

The number of revolutions made by drill is 0.5 sec is 8.32 revolutions.

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