# Physics

posted by .

To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration.
Suppose that a particle's position is given by the following expression:
r(t) = Rcos(omega*t)i + Rsin(omega*t)j

Velocity equals = -omegaR(sin(omega*t)i+omegaR(cos(omega*t)j

A. Now find the acceleration of the particle.
B. Your calculation is actually a derivation of the centripetal acceleration. To see this, express the acceleration of the particle in terms of its position r(t)

• Physics -

This is the obtuse way to find B.

you are given r(t)
velocity is dr/dt
acceleration is dv/dt

Hmmmm. It just got much simpler..prob states uniform circular motion, which means R is a constant. so R' =0, and angular velocity is constant (w'=0)
Then..
dv/dt=-w^2*R coswt i +w^2*R sinwt j
so there it is.
b) a=dv/dt=-w^2 * R(t) where the bold means a vector

## Similar Questions

1. ### physics

The angular position of a point on the rim of a rotating wheel is given by = 4.0t - 1.0t2 + t3, where is in radians and t is in seconds. (a) What is the angular velocity at t = 2 s?
2. ### Physics - angular acceleration

An object rotates about a fixed axis, and th angular position of a reference line on the object is given by THETA(t)=0.4e^2t, where THETA is in radians, and t is in seconds. [a.] what is the object's angular acceleration at t = 2 s?
3. ### Physics

A bicycle starts at the origin of a circular track that has a circumference of 126 m and travels at a constant speed a distance s = 38.0 m in a time t = 12s. a)what is the angular displacement (in rad) of the bicycle from its starting …
4. ### Maths mst

Question – 3: Consider a particle moving according to the velocity function, v(t) = 2a-3exp(-2t)+2/t+2,for t>0. (a) If the net distance,d,covered by the particle in the time interval,[0,3],is 20,find the value of a. What is the …
5. ### physics

A car engine accelerates at a constant rate from 170 rpm to 3050 rpm in 7 seconds. I have found that at t=0, the angular velocity (omega)=17.8 rad/s, the angular acceleration (alpha)= 43.1 rad/s^2, the tangential acceleration = 7.76 …
6. ### Physics

Uniform Circular Motion: Suppose that a particle's position is given by the following expression: r(t) = Rcos(omega*t)i + Rsin(omega*t)j 1. Choose the answer that best completes the following sentence: The particle's motion at t=0 …
7. ### college Physics

The coordinates of an object moving in the xy plane vary with time according to the following equations x = −7.16 sin ùt and y = 4.00 − 7.16 cos ùt, where ù is a constant, x and y are in meters, and t is in seconds. …
8. ### Physics

A particle moves along the x axis. It is initially at the position 0.350 m, moving with velocity 0.110 m/s and acceleration -0.380 m/s2. Suppose it moves with constant acceleration for 3.50 s. (a) Find the position of the particle …
9. ### science

An object moves up and down the y-axis with an acceleration given as a function of time t by the expression a equals A sine of omega-t. , whereA. and omega. are constants. What is the period of this motion?
10. ### physics

One of the conditions for Uniform Circular Motion is that the acceleration be centripetal and directed toward the center of motion. What would the effect be of a non-zero acceleration parallel to the tangential velocity?

More Similar Questions