The rod OA in Fig.1 rotates counterclockwise, its angular position (0) varies with time (t) according to Eq.1. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limacon described by Eq.2 () 14 exp(1 t+2 • (rad) (1) where t is in seconds. r = 8 – 15 cos(0) , (mm) (2 r = 100 (2 – cos 0) Figure 1: Prob.1 1. Derive an expression for 0(t) as a function to time. 2. Derive an expression for ŕ(t) as a function to time. 3. Derive an expression for 0(t) as a function to time. 4. Derive an expression for ř(t) as a function to time. 5. From the expressions accumulated over the last four questions, calculate the values of 0, r, 0, r, ô, ï At t = 1 (s). 6. Find the magnitude of the particle's velocity in (m/s) and its acceleration in (m/s²) at this instant.

The rod OA in Fig.1 rotates counterclockwise, its angular position (0) varies with time (t) according to Eq.1. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limacon described by Eq.2 () 14 exp(1 t+2 • (rad) (1) where t is in seconds. r = 8 – 15 cos(0) , (mm) (2 r = 100 (2 – cos 0) Figure 1: Prob.1 1. Derive an expression for 0(t) as a function to time. 2. Derive an expression for ŕ(t) as a function to time. 3. Derive an expression for 0(t) as a function to time. 4. Derive an expression for ř(t) as a function to time. 5. From the expressions accumulated over the last four questions, calculate the values of 0, r, 0, r, ô, ï At t = 1 (s). 6. Find the magnitude of the particle's velocity in (m/s) and its acceleration in (m/s²) at this instant.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

The rod OA in Fig.1 rotates counterclockwise, its angular position (0) varies with time (t) according to
Eq.1. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape
is a limacon described by Eq.2
(4)
G) exp(1 t+2 t?)
3
(rad)
(1)
where t is in seconds.
r = 8 – 15 cos(0) , (mm)
(2)
y
r = 100 (2 – cos 0)
Figure 1: Prob.1
1. Derive an expression for 0(t) as a function to time.
2. Derive an expression for r(t) as a function to time.
3. Derive an expression for 0(t) as a function to time.
4. Derive an expression for ř(t) as a function to time.
5. From the expressions accumulated over the last four questions, calculate the values of 0, r, 0, ř, ô, ï
At t = 1 (s).
6. Find the magnitude of the particle's velocity in (m/s) and its acceleration in (m/s²) at this instant.
1

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