Skip to main content
Ch 09: Rotation of Rigid Bodies
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 09: Rotation of Rigid BodiesProblem 24d
Chapter 9, Problem 24d

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2. What is the magnitude of the resultant acceleration of a point on the rim at t = 0.200 s?

Verified step by step guidance
1
Step 1: Convert the given angular velocity and angular acceleration from revolutions per second (rev/s) and revolutions per second squared (rev/s²) to radians per second (rad/s) and radians per second squared (rad/s²). Use the conversion factor: 1 revolution = 2π radians.
Step 2: Calculate the angular velocity at time t = 0.200 s using the formula \( \omega = \omega_0 + \alpha t \), where \( \omega_0 \) is the initial angular velocity, \( \alpha \) is the angular acceleration, and \( t \) is the time.
Step 3: Determine the tangential acceleration \( a_t \) of the point on the rim using the formula \( a_t = r \cdot \alpha \), where \( r \) is the radius of the turntable (half the diameter) and \( \alpha \) is the angular acceleration in radians per second squared.
Step 4: Calculate the centripetal acceleration \( a_c \) using the formula \( a_c = r \cdot \omega^2 \), where \( \omega \) is the angular velocity at time t = 0.200 s and \( r \) is the radius of the turntable.
Step 5: Find the magnitude of the resultant acceleration \( a_{res} \) by combining the tangential and centripetal accelerations using the Pythagorean theorem: \( a_{res} = \sqrt{a_t^2 + a_c^2} \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around an axis, expressed in radians per second or revolutions per second. In this question, the initial angular velocity of the turntable is given as 0.250 rev/s, indicating the rate at which the turntable is spinning at the start of the observation.
Recommended video:
Guided course
06:18
Intro to Angular Momentum

Angular Acceleration

Angular acceleration refers to the rate of change of angular velocity over time, typically measured in revolutions per second squared or radians per second squared. The constant angular acceleration of 0.900 rev/s² in this scenario indicates that the turntable's rotation speed is increasing uniformly, which is crucial for calculating the angular velocity at a specific time.
Recommended video:
Guided course
05:47
Intro to Acceleration

Resultant Acceleration

Resultant acceleration is the vector sum of tangential and centripetal accelerations acting on a point in circular motion. For a point on the rim of the turntable, tangential acceleration arises from angular acceleration, while centripetal acceleration is due to the circular path. Understanding both components is essential to determine the total acceleration at a given time.
Recommended video:
Guided course
05:47
Intro to Acceleration
Related Practice
Textbook Question

Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular to it and passing through (i) one end and (ii) its center, and (iii) about an axis parallel to the rod and passing through it.

2
views
Textbook Question

Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by extremely light rods (Fig. E9.28). Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O.

11
views
Textbook Question

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2.

(a) Compute the angular velocity of the turntable after 0.200 s.

(b) Through how many revolutions has the turntable spun in this time interval?

3
views
Textbook Question

A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s2. Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship arad = v2/r.

2
views
Textbook Question

A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis perpendicular to the bar through its center;

5
views
Textbook Question

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2. What is the tangential speed of a point on the rim of the turntable at t = 0.200 s?

5
views