Explanation Given: The radius of the disk and point A on the rim of the disk is shown in Figure (1). The angular velocity is ω = ( 5 t 2 + 2 ) rad/s . Time t is 0.5 s . From Figure (1) the radius r is 0.8 m . Write the equation of the angular velocity. ω = ( 5 t 2 + 2 ) rad/s (I) Here, angular acceleration is α . Write the expression for the magnitude of the velocity. υ A = ω r A (II) Here, velocity is υ A , angular velocity ω and radius is r A . Write the expression for the angular acceleration. α = d ω d t (III) Here, angular acceleration is α and rate of change of angular velocity with respect to time is ( d ω d t ) . Write the expression of tangential acceleration a t = α r A (IV) Here, tangential acceleration is a t , angular acceleration is α and radius is r A . Write the expression of normal acceleration a n = ω 2 r A (V) Here, normal acceleration is a n , angular velocity is ω and radius is r A . Write the expression for the magnitude of acceleration. a A = a t 2 + a n 2 (VI). Here, acceleration is a A , tangential acceleration is a t and normal acceleration is a n . Conclusion: Substitute ( 5 t 2 + 2 ) rad/s for ω in Equation (III). α = d ω d t = d d t ( 5 t 2 + 2 ) = 10 t (VII). Substitute 0.5 s for t in Equation (VII). α = 10 t = 10 ( 0.5 ) = 5 rad/s 2 Substitute 0

15th Edition

ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 16, Problem 1P

To determine

The magnitudes of the velocity and acceleration of a point A when time t is 0.5 s .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 6FP

Chapter 16, Problem 2P

Students have asked these similar questions

3. A 15% magnesium chloride solution is flowing through a 5-nom sch 40 commercial steel pipe at a rate of 325,000 lbm/h. The average temperature of the magnesium chloride solution as it flows through the pipe is 10°F. Determine the convective heat transfer coefficient inside the pipe.

2. Jojoba oil is flowing through a ¾-nom stainless steel pipe at a flow rate of 1,850 lbm/h. After the velocity profile in the pipe is fully developed, the oil enters a heater, as shown in Figure P5.7. The length of the heater section is 5 ft. The properties of the jojoba oil at the average temperature in the heater section are given in Table P5.7. Determine the convective heat transfer coefficient inside the heater section of the pipe. ¾ nom stainless steel pipe Heater section L=5ft Fig. P5.7 TABLE P5.7 Thermophysical Properties of Jojoba Oil at the Average Temperature in the Heater P (lbm/ft³) 68.671 (Btu/lbm-R) 0.30339 μ (lbm/ft-s) 0.012095 k (Btu/h-ft-°F) 0.077424

1. Water is flowing inside of a 3-std type K copper tube at a flow rate of 1.2 kg/s. The average temperature of the water is 50°C. Cold, dry air at a temperature of 5°C and atmospheric pressure flows outside of the tube in cross flow with a velocity of 85 m/s. Determine the UA product for this tube under clean conditions.

Chapter 16 Solutions

PEARSON ETEXT ENGINEERING MECH & STATS

Ch. 16 - When the gear rotates 20 revolutions, it achieves...Ch. 16 - The flywheel rotates with an angular velocity of ...Ch. 16 - The flywheel rotates with an angular velocity of (...Ch. 16 - The bucket is hoisted by the rope that wraps...Ch. 16 - A wheel has an angular acceleration of = (0.5 )...Ch. 16 - For a short period of time, the motor turns gear A...Ch. 16 - Prob. 1P Ch. 16 - The angular acceleration of the disk is defined by...Ch. 16 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16 - Prob. 4P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The magnitudes of the velocity and acceleration of a point A when time t is 0.5 s .

Solution Summary: The angular velocity and acceleration of a point A are shown in Figure (1).

Concept explainers

Videos

The magnitudes of the velocity and acceleration of a point A when time t is 0.5 s .

Want to see the full answer?

Chapter 16 Solutions