# Physics: centripetal acceleration, tangential acceleration, and angles?

Jeff of the Jungle swings on a vine that is 7.20m long (see the figure). At the bottom of the swing, just before hitting the tree, Jeff's linear speed is 8.5m/s. Suppose that at some point in his swing Jeff of the Jungle has an angular speed of 0.890rad/sec and an angular acceleration of 0.690rad/sec^2.

Find:

The magnitude of his centripetal acceleration in m/s^2.

The magnitude of his tangential acceleration in m/s^2.

The magnitude of the total acceleration in m/s^2.

The angle his total acceleration makes with respect to the tangential direction of motion in degrees.

Thanks!

### 1 Answer

- az_lenderLv 77 years agoBest answer
Centripetal acceleration = v^2/r

where v = (0.890 rad/sec)(7.20 m/rad) = 6.4 m/s;

centripetal acceleration = 5.7 m/s^2

Tangential acceleration = 0.690 rad/s^2 times (7.20 m/rad) = 4.97 m/s^2

Total acceleration = sqrt(5.7^2 + 4.97^2) m/s^2 = 7.56 m/s^2

Since the centripetal acceleration is larger than the tangential acceleration,

the direction of the total acceleration is closer to the direction of the centripetal acceleration

than it is to the direction of the tangential acceleration. The angle between the

total acceleration and the tangential acceleration is arctan(5.7/4.97) = 49 degrees